Ideals in $Z_{18}$
1
$begingroup$
Hello I am trying to find the ideals of Ideals in $Z_{18}$
I got confused so I looked at the back of the book which had
$<2>$ & $<3>$ as the answer and said they were both maximal and both prime.
I don't understand why $<2>$ & $<3>$ or how theyre both Maximal
EDIT: I don't understand Ideals in ring theory at all very well.
ring-theory
edited Dec 10 '18 at 1:50
Arturo Magidin
265k34590919
asked Dec 9 '18 at 23:17
TemirzhanTemirzhan
507314
$endgroup$
add a comment |
1
$begingroup$
Hello I am trying to find the ideals of Ideals in $Z_{18}$
I got confused so I looked at the back of the book which had
$<2>$ & $<3>$ as the answer and said they were both maximal and both prime.
I don't understand why $<2>$ & $<3>$ or how theyre both Maximal
EDIT: I don't understand Ideals in ring theory at all very well.
ring-theory
edited Dec 10 '18 at 1:50
Arturo Magidin
265k34590919
asked Dec 9 '18 at 23:17
TemirzhanTemirzhan
507314
$endgroup$
$begingroup$
I added the "ring-theory" tag to you post. Cheers!
$endgroup$
– Robert Lewis
Dec 9 '18 at 23:18
1
$begingroup$
Perhaps you should simply site down and write out these two ideals. There are only 18 elements in that ring, after all.
$endgroup$
– rschwieb
Dec 10 '18 at 0:01
$begingroup$
Do you know the isomorphism theorems? The ideals of $mathbb{Z}$ are well-known and understood, and the ideals of any quotient of $mathbb{Z}$ can be deduced from those of $mathbb{Z}$. PS This is not about groups.
$endgroup$
– Arturo Magidin
Dec 10 '18 at 1:50
add a comment |
1
1
1
$begingroup$
Hello I am trying to find the ideals of Ideals in $Z_{18}$
I got confused so I looked at the back of the book which had
$<2>$ & $<3>$ as the answer and said they were both maximal and both prime.
I don't understand why $<2>$ & $<3>$ or how theyre both Maximal
EDIT: I don't understand Ideals in ring theory at all very well.
ring-theory
edited Dec 10 '18 at 1:50
Arturo Magidin
265k34590919
asked Dec 9 '18 at 23:17
TemirzhanTemirzhan
507314
$endgroup$
Hello I am trying to find the ideals of Ideals in $Z_{18}$
I got confused so I looked at the back of the book which had
$<2>$ & $<3>$ as the answer and said they were both maximal and both prime.
I don't understand why $<2>$ & $<3>$ or how theyre both Maximal
EDIT: I don't understand Ideals in ring theory at all very well.
ring-theory
ring-theory
edited Dec 10 '18 at 1:50
Arturo Magidin
265k34590919
asked Dec 9 '18 at 23:17
TemirzhanTemirzhan
507314
edited Dec 10 '18 at 1:50
Arturo Magidin
265k34590919
asked Dec 9 '18 at 23:17
TemirzhanTemirzhan
507314
edited Dec 10 '18 at 1:50
Arturo Magidin
265k34590919
edited Dec 10 '18 at 1:50
Arturo Magidin
265k34590919
edited Dec 10 '18 at 1:50
Arturo Magidin
265k34590919
265k34590919
asked Dec 9 '18 at 23:17
TemirzhanTemirzhan
507314
asked Dec 9 '18 at 23:17
TemirzhanTemirzhan
507314
asked Dec 9 '18 at 23:17
TemirzhanTemirzhan
507314
507314
$begingroup$
I added the "ring-theory" tag to you post. Cheers!
$endgroup$
– Robert Lewis
Dec 9 '18 at 23:18
1
$begingroup$
Perhaps you should simply site down and write out these two ideals. There are only 18 elements in that ring, after all.
$endgroup$
– rschwieb
Dec 10 '18 at 0:01
$begingroup$
Do you know the isomorphism theorems? The ideals of $mathbb{Z}$ are well-known and understood, and the ideals of any quotient of $mathbb{Z}$ can be deduced from those of $mathbb{Z}$. PS This is not about groups.
$endgroup$
– Arturo Magidin
Dec 10 '18 at 1:50
add a comment |
$begingroup$
I added the "ring-theory" tag to you post. Cheers!
$endgroup$
– Robert Lewis
Dec 9 '18 at 23:18
1
$begingroup$
Perhaps you should simply site down and write out these two ideals. There are only 18 elements in that ring, after all.
$endgroup$
– rschwieb
Dec 10 '18 at 0:01
$begingroup$
Do you know the isomorphism theorems? The ideals of $mathbb{Z}$ are well-known and understood, and the ideals of any quotient of $mathbb{Z}$ can be deduced from those of $mathbb{Z}$. PS This is not about groups.
$endgroup$
– Arturo Magidin
Dec 10 '18 at 1:50
$begingroup$
I added the "ring-theory" tag to you post. Cheers!
$endgroup$
– Robert Lewis
Dec 9 '18 at 23:18
$begingroup$
I added the "ring-theory" tag to you post. Cheers!
$endgroup$
– Robert Lewis
Dec 9 '18 at 23:18
1
1
$begingroup$
Perhaps you should simply site down and write out these two ideals. There are only 18 elements in that ring, after all.
$endgroup$
– rschwieb
Dec 10 '18 at 0:01
$begingroup$
Perhaps you should simply site down and write out these two ideals. There are only 18 elements in that ring, after all.
$endgroup$
– rschwieb
Dec 10 '18 at 0:01
$begingroup$
Do you know the isomorphism theorems? The ideals of $mathbb{Z}$ are well-known and understood, and the ideals of any quotient of $mathbb{Z}$ can be deduced from those of $mathbb{Z}$. PS This is not about groups.
$endgroup$
– Arturo Magidin
Dec 10 '18 at 1:50
$begingroup$
Do you know the isomorphism theorems? The ideals of $mathbb{Z}$ are well-known and understood, and the ideals of any quotient of $mathbb{Z}$ can be deduced from those of $mathbb{Z}$. PS This is not about groups.
$endgroup$
– Arturo Magidin
Dec 10 '18 at 1:50
add a comment |
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$begingroup$
I added the "ring-theory" tag to you post. Cheers!
$endgroup$
– Robert Lewis
Dec 9 '18 at 23:18
1
$begingroup$
Perhaps you should simply site down and write out these two ideals. There are only 18 elements in that ring, after all.
$endgroup$
– rschwieb
Dec 10 '18 at 0:01
$begingroup$
Do you know the isomorphism theorems? The ideals of $mathbb{Z}$ are well-known and understood, and the ideals of any quotient of $mathbb{Z}$ can be deduced from those of $mathbb{Z}$. PS This is not about groups.
$endgroup$
– Arturo Magidin
Dec 10 '18 at 1:50