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Results tagged with modules
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user 38585
For questions on modules over rings.
1
vote
1
answer
297
views
Is this square commutative?
Suppose that the following commutative diagram of $R$-modules is given. …
- 141
1
vote
1
answer
354
views
Pure monomorphism of functors-
Question: There is a natural transformation $\eta^+: G^+\rightarrow F^+$ such that for each object $v$ of $Q$ we have a split epimorphism $G^+(v)\rightarrow F^+(v)$ of modules. …
- 141
2
votes
1
answer
169
views
pure sub-complexes of exact subcomplexes
In https://www.google.com/#q=tensor+product+of+complexes%2Benochs a new tensor product of complexes is defined which characterizes flatness in the category of complexes of $R$-modules. … Question: Let $\varepsilon$ be the class of all exact complexes of $R$-modules. IS $\varepsilon$ is closed under pure sub-complexes? (That is pure subcomplexes of exact complexes are exact). …
- 141
4
votes
1
answer
480
views
Splitness of commutative diagrams
Consider the following commutative diagram in the category of $R$-modules where $R$ is an associative ring with identity and all modules are unital.
$
\newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1 …
- 141
2
votes
1
answer
180
views
dg-flat complexes and their characters
Let $\otimes$ denotes the usual tensor products of complexes and symbols live in the category of chain complexes of $R$-modules. Let $X$ be a dg-flat complex (i.e. …
- 141
1
vote
1
answer
277
views
finitely presented representations
$X$ is called a representation of Q by modules if it is a functor from Q to R-Mod. i.e. … It is proved that $(Q, R-Mod)$, the category of representations of Q by R-modules, is equivalent to the category of RQ-modules whenever RQ is a path ring associated to $Q$. …
- 141