Answer by Zev Chonoles for A statement on exact sequences of R-modules.
If $h:P\to Q$ is a homomorphism of some sort (of groups, modules, rings, etc.), then the statement that $h$ induces a homomorphism $\widetilde{h}:P/S\to Q$ for a given subobject $S$ of $P$ (subgroup,...
View ArticleAnswer by Rafael Holanda for A statement on exact sequences of R-modules.
"g "induces"" means that the map $$\begin{matrix}B/Im(f)&\longrightarrow&C\\\overline{x}&\longmapsto&g(x)\end{matrix}$$ is an isomorphism.Now, given $y\in Im(f)$ then...
View ArticleA statement on exact sequences of R-modules.
My question is related to the answer of this post:Exact sequence of $A$-modules.I am trying to understand this answer, but I am stuck at the following statement.Given is a sequence $A\stackrel...
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