Every R-module $M$ has a maximal linearly independent subset $A$. If submodule $M_A$ is generated by $A$,...
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I am stuck at proving
Every R-module $M$ has a maximal linearly independent subset $A$. If a submodule $M_A$ is generated by $A$, then $M_A$ is free on $A$, and for a submodule $M_1subseteq M$, $M_1 cap M_A neq 0$.
I know for the first part I should just apply Zorn's lemma, but I am not clear about the rest of the problem. Could anyone help me with that?
abstract-algebra modules free-modules
asked Nov 16 at 5:46
Eric Curtis
213
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up vote
1
down vote
favorite
I am stuck at proving
Every R-module $M$ has a maximal linearly independent subset $A$. If a submodule $M_A$ is generated by $A$, then $M_A$ is free on $A$, and for a submodule $M_1subseteq M$, $M_1 cap M_A neq 0$.
I know for the first part I should just apply Zorn's lemma, but I am not clear about the rest of the problem. Could anyone help me with that?
abstract-algebra modules free-modules
asked Nov 16 at 5:46
Eric Curtis
213
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am stuck at proving
Every R-module $M$ has a maximal linearly independent subset $A$. If a submodule $M_A$ is generated by $A$, then $M_A$ is free on $A$, and for a submodule $M_1subseteq M$, $M_1 cap M_A neq 0$.
I know for the first part I should just apply Zorn's lemma, but I am not clear about the rest of the problem. Could anyone help me with that?
abstract-algebra modules free-modules
asked Nov 16 at 5:46
Eric Curtis
213
I am stuck at proving
Every R-module $M$ has a maximal linearly independent subset $A$. If a submodule $M_A$ is generated by $A$, then $M_A$ is free on $A$, and for a submodule $M_1subseteq M$, $M_1 cap M_A neq 0$.
I know for the first part I should just apply Zorn's lemma, but I am not clear about the rest of the problem. Could anyone help me with that?
abstract-algebra modules free-modules
abstract-algebra modules free-modules
asked Nov 16 at 5:46
Eric Curtis
213
asked Nov 16 at 5:46
Eric Curtis
213
asked Nov 16 at 5:46
Eric Curtis
213
asked Nov 16 at 5:46
Eric Curtis
213
asked Nov 16 at 5:46
Eric Curtis
213
213
add a comment |
add a comment |
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