How do you write this module as a direct sum of cyclic modules?
0
$begingroup$
Let M be the module over Z [i] generated by elements x, y whose relations are determined by $(1+i)x+(2-i)y=0$ and $3x+5y=0$. How can one write M as a direct sum of cyclic modules?
abstract-algebra modules
edited Dec 2 '18 at 0:42
rschwieb
106k12102250
asked Dec 1 '18 at 20:23
Mike HawkMike Hawk
61
$endgroup$
|
show 1 more comment
0
$begingroup$
Let M be the module over Z [i] generated by elements x, y whose relations are determined by $(1+i)x+(2-i)y=0$ and $3x+5y=0$. How can one write M as a direct sum of cyclic modules?
abstract-algebra modules
edited Dec 2 '18 at 0:42
rschwieb
106k12102250
asked Dec 1 '18 at 20:23
Mike HawkMike Hawk
61
$endgroup$
1
$begingroup$
Hey, and welcome to M.SE! To help you, it is helpful to know what you have tried, what your background is (e.g., are you comfortable with the notion of direct sum and cyclic module?), and what your process of thinking was when you approached this question.
$endgroup$
– Luke
Dec 1 '18 at 20:42
$begingroup$
@Luke, I'm learning modules for the first time. So that, when I think of a module I'm always with the generalization of a vector space. When I think of direct sum I always think on the linear combination of linearly independent generators of subspaces. But I don't know how can I relate this thinking with that question.
$endgroup$
– Mike Hawk
Dec 1 '18 at 22:29
$begingroup$
@MikeHawk you seem to have confused the title field for the tags field. I changed the title to be more useful. You should do something like that next time. Remember, the goal is to be informative and searchable. If you don’t, well, you’ll probably find out what the consequences are. Good luck.
$endgroup$
– rschwieb
Dec 2 '18 at 0:43
$begingroup$
Thank you @rschwieb
$endgroup$
– Mike Hawk
Dec 2 '18 at 0:56
$begingroup$
Similar to these: 1, 2, 3
$endgroup$
– André 3000
Dec 2 '18 at 8:39
|
show 1 more comment
0
0
0
$begingroup$
Let M be the module over Z [i] generated by elements x, y whose relations are determined by $(1+i)x+(2-i)y=0$ and $3x+5y=0$. How can one write M as a direct sum of cyclic modules?
abstract-algebra modules
edited Dec 2 '18 at 0:42
rschwieb
106k12102250
asked Dec 1 '18 at 20:23
Mike HawkMike Hawk
61
$endgroup$
Let M be the module over Z [i] generated by elements x, y whose relations are determined by $(1+i)x+(2-i)y=0$ and $3x+5y=0$. How can one write M as a direct sum of cyclic modules?
abstract-algebra modules
abstract-algebra modules
edited Dec 2 '18 at 0:42
rschwieb
106k12102250
asked Dec 1 '18 at 20:23
Mike HawkMike Hawk
61
edited Dec 2 '18 at 0:42
rschwieb
106k12102250
asked Dec 1 '18 at 20:23
Mike HawkMike Hawk
61
edited Dec 2 '18 at 0:42
rschwieb
106k12102250
edited Dec 2 '18 at 0:42
rschwieb
106k12102250
edited Dec 2 '18 at 0:42
rschwieb
106k12102250
106k12102250
asked Dec 1 '18 at 20:23
Mike HawkMike Hawk
61
asked Dec 1 '18 at 20:23
Mike HawkMike Hawk
61
asked Dec 1 '18 at 20:23
Mike HawkMike Hawk
61
61
1
$begingroup$
Hey, and welcome to M.SE! To help you, it is helpful to know what you have tried, what your background is (e.g., are you comfortable with the notion of direct sum and cyclic module?), and what your process of thinking was when you approached this question.
$endgroup$
– Luke
Dec 1 '18 at 20:42
$begingroup$
@Luke, I'm learning modules for the first time. So that, when I think of a module I'm always with the generalization of a vector space. When I think of direct sum I always think on the linear combination of linearly independent generators of subspaces. But I don't know how can I relate this thinking with that question.
$endgroup$
– Mike Hawk
Dec 1 '18 at 22:29
$begingroup$
@MikeHawk you seem to have confused the title field for the tags field. I changed the title to be more useful. You should do something like that next time. Remember, the goal is to be informative and searchable. If you don’t, well, you’ll probably find out what the consequences are. Good luck.
$endgroup$
– rschwieb
Dec 2 '18 at 0:43
$begingroup$
Thank you @rschwieb
$endgroup$
– Mike Hawk
Dec 2 '18 at 0:56
$begingroup$
Similar to these: 1, 2, 3
$endgroup$
– André 3000
Dec 2 '18 at 8:39
|
show 1 more comment
1
$begingroup$
Hey, and welcome to M.SE! To help you, it is helpful to know what you have tried, what your background is (e.g., are you comfortable with the notion of direct sum and cyclic module?), and what your process of thinking was when you approached this question.
$endgroup$
– Luke
Dec 1 '18 at 20:42
$begingroup$
@Luke, I'm learning modules for the first time. So that, when I think of a module I'm always with the generalization of a vector space. When I think of direct sum I always think on the linear combination of linearly independent generators of subspaces. But I don't know how can I relate this thinking with that question.
$endgroup$
– Mike Hawk
Dec 1 '18 at 22:29
$begingroup$
@MikeHawk you seem to have confused the title field for the tags field. I changed the title to be more useful. You should do something like that next time. Remember, the goal is to be informative and searchable. If you don’t, well, you’ll probably find out what the consequences are. Good luck.
$endgroup$
– rschwieb
Dec 2 '18 at 0:43
$begingroup$
Thank you @rschwieb
$endgroup$
– Mike Hawk
Dec 2 '18 at 0:56
$begingroup$
Similar to these: 1, 2, 3
$endgroup$
– André 3000
Dec 2 '18 at 8:39
1
1
$begingroup$
Hey, and welcome to M.SE! To help you, it is helpful to know what you have tried, what your background is (e.g., are you comfortable with the notion of direct sum and cyclic module?), and what your process of thinking was when you approached this question.
$endgroup$
– Luke
Dec 1 '18 at 20:42
$begingroup$
Hey, and welcome to M.SE! To help you, it is helpful to know what you have tried, what your background is (e.g., are you comfortable with the notion of direct sum and cyclic module?), and what your process of thinking was when you approached this question.
$endgroup$
– Luke
Dec 1 '18 at 20:42
$begingroup$
@Luke, I'm learning modules for the first time. So that, when I think of a module I'm always with the generalization of a vector space. When I think of direct sum I always think on the linear combination of linearly independent generators of subspaces. But I don't know how can I relate this thinking with that question.
$endgroup$
– Mike Hawk
Dec 1 '18 at 22:29
$begingroup$
@Luke, I'm learning modules for the first time. So that, when I think of a module I'm always with the generalization of a vector space. When I think of direct sum I always think on the linear combination of linearly independent generators of subspaces. But I don't know how can I relate this thinking with that question.
$endgroup$
– Mike Hawk
Dec 1 '18 at 22:29
$begingroup$
@MikeHawk you seem to have confused the title field for the tags field. I changed the title to be more useful. You should do something like that next time. Remember, the goal is to be informative and searchable. If you don’t, well, you’ll probably find out what the consequences are. Good luck.
$endgroup$
– rschwieb
Dec 2 '18 at 0:43
$begingroup$
@MikeHawk you seem to have confused the title field for the tags field. I changed the title to be more useful. You should do something like that next time. Remember, the goal is to be informative and searchable. If you don’t, well, you’ll probably find out what the consequences are. Good luck.
$endgroup$
– rschwieb
Dec 2 '18 at 0:43
$begingroup$
Thank you @rschwieb
$endgroup$
– Mike Hawk
Dec 2 '18 at 0:56
$begingroup$
Thank you @rschwieb
$endgroup$
– Mike Hawk
Dec 2 '18 at 0:56
$begingroup$
Similar to these: 1, 2, 3
$endgroup$
– André 3000
Dec 2 '18 at 8:39
$begingroup$
Similar to these: 1, 2, 3
$endgroup$
– André 3000
Dec 2 '18 at 8:39
|
show 1 more comment
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1
$begingroup$
Hey, and welcome to M.SE! To help you, it is helpful to know what you have tried, what your background is (e.g., are you comfortable with the notion of direct sum and cyclic module?), and what your process of thinking was when you approached this question.
$endgroup$
– Luke
Dec 1 '18 at 20:42
$begingroup$
@Luke, I'm learning modules for the first time. So that, when I think of a module I'm always with the generalization of a vector space. When I think of direct sum I always think on the linear combination of linearly independent generators of subspaces. But I don't know how can I relate this thinking with that question.
$endgroup$
– Mike Hawk
Dec 1 '18 at 22:29
$begingroup$
@MikeHawk you seem to have confused the title field for the tags field. I changed the title to be more useful. You should do something like that next time. Remember, the goal is to be informative and searchable. If you don’t, well, you’ll probably find out what the consequences are. Good luck.
$endgroup$
– rschwieb
Dec 2 '18 at 0:43
$begingroup$
Thank you @rschwieb
$endgroup$
– Mike Hawk
Dec 2 '18 at 0:56
$begingroup$
Similar to these: 1, 2, 3
$endgroup$
– André 3000
Dec 2 '18 at 8:39