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Results tagged with modules
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user 461
For questions on modules over rings.
4
votes
0
answers
486
views
Endomorphisms of free modules and extension of scalars
Let $B$ be a commutative ring with $1$, let $A$ be a subring such that any unit of $B$ which belongs to $A$ is a unit of $A$, and let $\phi:F\to F$ be an endomorphism of a free $A$-modules $F$ such that …
- 4,416
5
votes
0
answers
101
views
Is there a positive integer k such that any endomorphism of any free module over any commuta...
Consider the following Condition (C) on a positive integer $k$:
(C) If $R$ is a commutative ring, if $F$ is a free $R$-module, and if $f$ is an endomorphism of $F$, then $f$ is an $R$-linear combinat …
CommunityBot
- 1
17
votes
Accepted
"Sums-compact" objects = f.g. objects in categories of modules?
Trlifaj, Dually slender modules and steady rings, Forum Math. 9 (1997), 61-74.
This paper is available online, but I don't understand it:
Jan Zemlicka, Classes of dually slender modules, Proc. … Rentschler, Sur les modules M tels que $\text{Hom}(M,-)$ commute avec les sommes directes, C. R. Acad. Sci. Paris Sér. …
CommunityBot
- 1
1
vote
0
answers
127
views
Preservation of direct sums and finite generation
The second question is:
Do uncountably cofinal modules exist? …
CommunityBot
- 1