All Questions
8 questions
7
votes
0
answers
275
views
Split epimorphism of modules - does the finite case imply the infinite case?
Let $k$ be a field, $A$ a finite dimensional $k$-algebra, $X$ a finite dimensional indecomposable (left) $A$-module and $M$ an infinite dimensional (left) $A$-module. Suppose further we have an ...
- 696
3
votes
1
answer
240
views
Split monomorphisms of modules - does the finite case imply the infinite case?
Let $k$ be a field, $A$ a finite dimensional $k$-algebra, $X$ a finite dimensional indecomposable (left) $A$-module and $M$ an infinite dimensional (left) $A$-module. Further $X\subseteq M$ and for ...
- 696
5
votes
1
answer
234
views
Concept of an exact ideal of a module category
Let $R$ be a ring and $\text{Mod}\,R$ the category of (left) $R$-modules. Consider an ideal $\mathcal{I}$ of $\text{Mod}\,R$. For $R$-modules $X$ and $Y$ let $\mathcal{I}(X,Y)$ be the collection of ...
- 696
4
votes
0
answers
187
views
Generalization of the second Brauer-Thrall conjecture for arbitrary Artin algebras
Let $k$ be a field with infinite cardinality and $A$ a finite dimensional $k$-Algebra. The second Brauer-Thrall conjecture states the following: There are infinitely many natural numbers $n_1<n_2&...
- 696
6
votes
3
answers
446
views
Is the category of symmetric bimodules over a commutative ring closed under extensions?
Let $A$ be a commutative ring, and consider the category of bimodules over $A$.
An $A$-bimodule $M$ is called symmetric if $a\cdot m = m \cdot a$ for all $a \in A$, $m \in M$.
Is the category of ...
- 61
1
vote
2
answers
337
views
Finding all submodules
Given a finite dimensional local commutative algebra over a finite field $K$ and a finite dimensional module $M$. What is the fastest/best way to obtain all submodule from $M$ using a Computer algebra ...
- 26.5k
4
votes
1
answer
382
views
Non-existence of projective covers
I didn't get the argument of Example 7.3.11, page 123, from the representation theory book of Peter Webb, available also online at:
http://www-users.math.umn.edu/~webb/RepBook/RepBookLatex.pdf
In ...
- 137
2
votes
1
answer
395
views
Projectivity of torsion-free modules over integral group rings
Let $G$ be a torsion-free group and assume that the integral group ring $\mathbb{Z}G$ is torsion-free as well. Let $M$ be a torsion-free, finitely generated module over $\mathbb{Z}G$.
If we assume ...
- 2,998