Algebra - rings $2mathbb Z$ and $mathbb Z_3$ [closed]
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Can anyone tell what's the difference between these two rings: $2mathbb Z$ and $mathbb Z_3$ ?
I think that ring $2mathbb Z$ represents remainders when dividing with two, can anyone help? Thanks for your time!
abstract-algebra ring-theory
edited Dec 7 '18 at 18:30
Batominovski
33.1k33293
asked Dec 6 '18 at 18:04
HausHaus
307
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closed as unclear what you're asking by Crostul, rschwieb, Jyrki Lahtonen, Lord Shark the Unknown, KReiser Dec 7 '18 at 8:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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$begingroup$
Can anyone tell what's the difference between these two rings: $2mathbb Z$ and $mathbb Z_3$ ?
I think that ring $2mathbb Z$ represents remainders when dividing with two, can anyone help? Thanks for your time!
abstract-algebra ring-theory
edited Dec 7 '18 at 18:30
Batominovski
33.1k33293
asked Dec 6 '18 at 18:04
HausHaus
307
$endgroup$
closed as unclear what you're asking by Crostul, rschwieb, Jyrki Lahtonen, Lord Shark the Unknown, KReiser Dec 7 '18 at 8:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
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Do you mean $2Bbb Z$ and $Bbb Z_3$? Or $Bbb Z^3$? Or $3Bbb Z$? Or something else?
$endgroup$
– Arthur
Dec 6 '18 at 18:06
1
$begingroup$
@Haus ...... and it is not any of those Arthur listed? Surely you could say which ones were the relevant ones, if so. The way to type those, respectively is$2mathbb Z$$mathbb Z_3$$mathbb Z^3$and$3mathbb Z$
$endgroup$
– rschwieb
Dec 6 '18 at 18:12
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$2mathbb Z$ and $mathbb Z_3$.
$endgroup$
– Haus
Dec 6 '18 at 18:15
1
$begingroup$
@Haus Whenever you are asked for clarification, you can respond in the comments, but then you should also fix your question. Use the edit button.
$endgroup$
– rschwieb
Dec 6 '18 at 18:18
1
$begingroup$
Thank you. I am still learning how to write tasks here.
$endgroup$
– Haus
Dec 6 '18 at 18:20
|
show 1 more comment
$begingroup$
Can anyone tell what's the difference between these two rings: $2mathbb Z$ and $mathbb Z_3$ ?
I think that ring $2mathbb Z$ represents remainders when dividing with two, can anyone help? Thanks for your time!
abstract-algebra ring-theory
edited Dec 7 '18 at 18:30
Batominovski
33.1k33293
asked Dec 6 '18 at 18:04
HausHaus
307
$endgroup$
Can anyone tell what's the difference between these two rings: $2mathbb Z$ and $mathbb Z_3$ ?
I think that ring $2mathbb Z$ represents remainders when dividing with two, can anyone help? Thanks for your time!
abstract-algebra ring-theory
abstract-algebra ring-theory
edited Dec 7 '18 at 18:30
Batominovski
33.1k33293
asked Dec 6 '18 at 18:04
HausHaus
307
edited Dec 7 '18 at 18:30
Batominovski
33.1k33293
asked Dec 6 '18 at 18:04
HausHaus
307
edited Dec 7 '18 at 18:30
Batominovski
33.1k33293
edited Dec 7 '18 at 18:30
Batominovski
33.1k33293
edited Dec 7 '18 at 18:30
Batominovski
33.1k33293
33.1k33293
asked Dec 6 '18 at 18:04
HausHaus
307
asked Dec 6 '18 at 18:04
HausHaus
307
asked Dec 6 '18 at 18:04
HausHaus
307
307
closed as unclear what you're asking by Crostul, rschwieb, Jyrki Lahtonen, Lord Shark the Unknown, KReiser Dec 7 '18 at 8:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Crostul, rschwieb, Jyrki Lahtonen, Lord Shark the Unknown, KReiser Dec 7 '18 at 8:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
$begingroup$
Do you mean $2Bbb Z$ and $Bbb Z_3$? Or $Bbb Z^3$? Or $3Bbb Z$? Or something else?
$endgroup$
– Arthur
Dec 6 '18 at 18:06
1
$begingroup$
@Haus ...... and it is not any of those Arthur listed? Surely you could say which ones were the relevant ones, if so. The way to type those, respectively is$2mathbb Z$$mathbb Z_3$$mathbb Z^3$and$3mathbb Z$
$endgroup$
– rschwieb
Dec 6 '18 at 18:12
$begingroup$
$2mathbb Z$ and $mathbb Z_3$.
$endgroup$
– Haus
Dec 6 '18 at 18:15
1
$begingroup$
@Haus Whenever you are asked for clarification, you can respond in the comments, but then you should also fix your question. Use the edit button.
$endgroup$
– rschwieb
Dec 6 '18 at 18:18
1
$begingroup$
Thank you. I am still learning how to write tasks here.
$endgroup$
– Haus
Dec 6 '18 at 18:20
|
show 1 more comment
2
$begingroup$
Do you mean $2Bbb Z$ and $Bbb Z_3$? Or $Bbb Z^3$? Or $3Bbb Z$? Or something else?
$endgroup$
– Arthur
Dec 6 '18 at 18:06
1
$begingroup$
@Haus ...... and it is not any of those Arthur listed? Surely you could say which ones were the relevant ones, if so. The way to type those, respectively is$2mathbb Z$$mathbb Z_3$$mathbb Z^3$and$3mathbb Z$
$endgroup$
– rschwieb
Dec 6 '18 at 18:12
$begingroup$
$2mathbb Z$ and $mathbb Z_3$.
$endgroup$
– Haus
Dec 6 '18 at 18:15
1
$begingroup$
@Haus Whenever you are asked for clarification, you can respond in the comments, but then you should also fix your question. Use the edit button.
$endgroup$
– rschwieb
Dec 6 '18 at 18:18
1
$begingroup$
Thank you. I am still learning how to write tasks here.
$endgroup$
– Haus
Dec 6 '18 at 18:20
2
2
$begingroup$
Do you mean $2Bbb Z$ and $Bbb Z_3$? Or $Bbb Z^3$? Or $3Bbb Z$? Or something else?
$endgroup$
– Arthur
Dec 6 '18 at 18:06
$begingroup$
Do you mean $2Bbb Z$ and $Bbb Z_3$? Or $Bbb Z^3$? Or $3Bbb Z$? Or something else?
$endgroup$
– Arthur
Dec 6 '18 at 18:06
1
1
$begingroup$
@Haus ...... and it is not any of those Arthur listed? Surely you could say which ones were the relevant ones, if so. The way to type those, respectively is
$2mathbb Z$ $mathbb Z_3$ $mathbb Z^3$ and $3mathbb Z$$endgroup$
– rschwieb
Dec 6 '18 at 18:12
$begingroup$
@Haus ...... and it is not any of those Arthur listed? Surely you could say which ones were the relevant ones, if so. The way to type those, respectively is
$2mathbb Z$ $mathbb Z_3$ $mathbb Z^3$ and $3mathbb Z$$endgroup$
– rschwieb
Dec 6 '18 at 18:12
$begingroup$
$2mathbb Z$ and $mathbb Z_3$.
$endgroup$
– Haus
Dec 6 '18 at 18:15
$begingroup$
$2mathbb Z$ and $mathbb Z_3$.
$endgroup$
– Haus
Dec 6 '18 at 18:15
1
1
$begingroup$
@Haus Whenever you are asked for clarification, you can respond in the comments, but then you should also fix your question. Use the edit button.
$endgroup$
– rschwieb
Dec 6 '18 at 18:18
$begingroup$
@Haus Whenever you are asked for clarification, you can respond in the comments, but then you should also fix your question. Use the edit button.
$endgroup$
– rschwieb
Dec 6 '18 at 18:18
1
1
$begingroup$
Thank you. I am still learning how to write tasks here.
$endgroup$
– Haus
Dec 6 '18 at 18:20
$begingroup$
Thank you. I am still learning how to write tasks here.
$endgroup$
– Haus
Dec 6 '18 at 18:20
|
show 1 more comment
1 Answer
1
active
oldest
votes
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$2Bbb Z $ is the set of all multiples of $2$ whereas $Bbb{Z}_3$ is the set of all equivalence classes under the relation $text{R}$ on $Bbb Z $ such that $atext{R}b $ if and only if $3|(b-a) $.
Edit: $mathbb Z_3$ is also the standard notation for $3$-adic integers.
Courtesy :@rschwieb
answered Dec 6 '18 at 18:13
Thomas ShelbyThomas Shelby
3,7342625
$endgroup$
2
$begingroup$
Some people are going to complain that $mathbb Z_3$ is also standard notation for $3$-adic integers, so you should probably also add that.
$endgroup$
– rschwieb
Dec 6 '18 at 18:17
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@rschwieb I'm completely ignorant of the meaning/definition of $3$-adic integers.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:22
1
$begingroup$
en.wikipedia.org/wiki/P-adic_number Well, if you feel like improving your answer and hedging against that, there you go. I'm not really sure you'd need to do anything more than mention it, if you wanted.
$endgroup$
– rschwieb
Dec 6 '18 at 18:23
$begingroup$
@rschwieb Thank you for your suggestion. I've edited my answer.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:30
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$2Bbb Z $ is the set of all multiples of $2$ whereas $Bbb{Z}_3$ is the set of all equivalence classes under the relation $text{R}$ on $Bbb Z $ such that $atext{R}b $ if and only if $3|(b-a) $.
Edit: $mathbb Z_3$ is also the standard notation for $3$-adic integers.
Courtesy :@rschwieb
answered Dec 6 '18 at 18:13
Thomas ShelbyThomas Shelby
3,7342625
$endgroup$
2
$begingroup$
Some people are going to complain that $mathbb Z_3$ is also standard notation for $3$-adic integers, so you should probably also add that.
$endgroup$
– rschwieb
Dec 6 '18 at 18:17
$begingroup$
@rschwieb I'm completely ignorant of the meaning/definition of $3$-adic integers.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:22
1
$begingroup$
en.wikipedia.org/wiki/P-adic_number Well, if you feel like improving your answer and hedging against that, there you go. I'm not really sure you'd need to do anything more than mention it, if you wanted.
$endgroup$
– rschwieb
Dec 6 '18 at 18:23
$begingroup$
@rschwieb Thank you for your suggestion. I've edited my answer.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:30
add a comment |
$begingroup$
$2Bbb Z $ is the set of all multiples of $2$ whereas $Bbb{Z}_3$ is the set of all equivalence classes under the relation $text{R}$ on $Bbb Z $ such that $atext{R}b $ if and only if $3|(b-a) $.
Edit: $mathbb Z_3$ is also the standard notation for $3$-adic integers.
Courtesy :@rschwieb
answered Dec 6 '18 at 18:13
Thomas ShelbyThomas Shelby
3,7342625
$endgroup$
2
$begingroup$
Some people are going to complain that $mathbb Z_3$ is also standard notation for $3$-adic integers, so you should probably also add that.
$endgroup$
– rschwieb
Dec 6 '18 at 18:17
$begingroup$
@rschwieb I'm completely ignorant of the meaning/definition of $3$-adic integers.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:22
1
$begingroup$
en.wikipedia.org/wiki/P-adic_number Well, if you feel like improving your answer and hedging against that, there you go. I'm not really sure you'd need to do anything more than mention it, if you wanted.
$endgroup$
– rschwieb
Dec 6 '18 at 18:23
$begingroup$
@rschwieb Thank you for your suggestion. I've edited my answer.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:30
add a comment |
$begingroup$
$2Bbb Z $ is the set of all multiples of $2$ whereas $Bbb{Z}_3$ is the set of all equivalence classes under the relation $text{R}$ on $Bbb Z $ such that $atext{R}b $ if and only if $3|(b-a) $.
Edit: $mathbb Z_3$ is also the standard notation for $3$-adic integers.
Courtesy :@rschwieb
answered Dec 6 '18 at 18:13
Thomas ShelbyThomas Shelby
3,7342625
$endgroup$
$2Bbb Z $ is the set of all multiples of $2$ whereas $Bbb{Z}_3$ is the set of all equivalence classes under the relation $text{R}$ on $Bbb Z $ such that $atext{R}b $ if and only if $3|(b-a) $.
Edit: $mathbb Z_3$ is also the standard notation for $3$-adic integers.
Courtesy :@rschwieb
answered Dec 6 '18 at 18:13
Thomas ShelbyThomas Shelby
3,7342625
edited Dec 6 '18 at 18:29
answered Dec 6 '18 at 18:13
Thomas ShelbyThomas Shelby
3,7342625
answered Dec 6 '18 at 18:13
Thomas ShelbyThomas Shelby
3,7342625
answered Dec 6 '18 at 18:13
Thomas ShelbyThomas Shelby
3,7342625
3,7342625
2
$begingroup$
Some people are going to complain that $mathbb Z_3$ is also standard notation for $3$-adic integers, so you should probably also add that.
$endgroup$
– rschwieb
Dec 6 '18 at 18:17
$begingroup$
@rschwieb I'm completely ignorant of the meaning/definition of $3$-adic integers.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:22
1
$begingroup$
en.wikipedia.org/wiki/P-adic_number Well, if you feel like improving your answer and hedging against that, there you go. I'm not really sure you'd need to do anything more than mention it, if you wanted.
$endgroup$
– rschwieb
Dec 6 '18 at 18:23
$begingroup$
@rschwieb Thank you for your suggestion. I've edited my answer.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:30
add a comment |
2
$begingroup$
Some people are going to complain that $mathbb Z_3$ is also standard notation for $3$-adic integers, so you should probably also add that.
$endgroup$
– rschwieb
Dec 6 '18 at 18:17
$begingroup$
@rschwieb I'm completely ignorant of the meaning/definition of $3$-adic integers.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:22
1
$begingroup$
en.wikipedia.org/wiki/P-adic_number Well, if you feel like improving your answer and hedging against that, there you go. I'm not really sure you'd need to do anything more than mention it, if you wanted.
$endgroup$
– rschwieb
Dec 6 '18 at 18:23
$begingroup$
@rschwieb Thank you for your suggestion. I've edited my answer.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:30
2
2
$begingroup$
Some people are going to complain that $mathbb Z_3$ is also standard notation for $3$-adic integers, so you should probably also add that.
$endgroup$
– rschwieb
Dec 6 '18 at 18:17
$begingroup$
Some people are going to complain that $mathbb Z_3$ is also standard notation for $3$-adic integers, so you should probably also add that.
$endgroup$
– rschwieb
Dec 6 '18 at 18:17
$begingroup$
@rschwieb I'm completely ignorant of the meaning/definition of $3$-adic integers.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:22
$begingroup$
@rschwieb I'm completely ignorant of the meaning/definition of $3$-adic integers.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:22
1
1
$begingroup$
en.wikipedia.org/wiki/P-adic_number Well, if you feel like improving your answer and hedging against that, there you go. I'm not really sure you'd need to do anything more than mention it, if you wanted.
$endgroup$
– rschwieb
Dec 6 '18 at 18:23
$begingroup$
en.wikipedia.org/wiki/P-adic_number Well, if you feel like improving your answer and hedging against that, there you go. I'm not really sure you'd need to do anything more than mention it, if you wanted.
$endgroup$
– rschwieb
Dec 6 '18 at 18:23
$begingroup$
@rschwieb Thank you for your suggestion. I've edited my answer.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:30
$begingroup$
@rschwieb Thank you for your suggestion. I've edited my answer.
$endgroup$
– Thomas Shelby
Dec 6 '18 at 18:30
add a comment |
2
$begingroup$
Do you mean $2Bbb Z$ and $Bbb Z_3$? Or $Bbb Z^3$? Or $3Bbb Z$? Or something else?
$endgroup$
– Arthur
Dec 6 '18 at 18:06
1
$begingroup$
@Haus ...... and it is not any of those Arthur listed? Surely you could say which ones were the relevant ones, if so. The way to type those, respectively is
$2mathbb Z$$mathbb Z_3$$mathbb Z^3$and$3mathbb Z$$endgroup$
– rschwieb
Dec 6 '18 at 18:12
$begingroup$
$2mathbb Z$ and $mathbb Z_3$.
$endgroup$
– Haus
Dec 6 '18 at 18:15
1
$begingroup$
@Haus Whenever you are asked for clarification, you can respond in the comments, but then you should also fix your question. Use the edit button.
$endgroup$
– rschwieb
Dec 6 '18 at 18:18
1
$begingroup$
Thank you. I am still learning how to write tasks here.
$endgroup$
– Haus
Dec 6 '18 at 18:20