Skip to main content
Mathematics
Liang Chen's user avatar
Liang Chen's user avatar
Liang Chen's user avatar
Liang Chen
  • Member for 2 years, 10 months
  • Last seen this week
Profile Activity
Stats
963
reputation
5k
reached
18
answers
42
questions
Communities
Badges
View all badges
This user doesn’t have any gold badges yet.
3
silver badges
13
bronze badges
Top tags
View all tags
6
Score
24
Posts
40
Posts %
3
Score
13
Posts
22
Posts %
3
Score
8
Posts
13
Posts %
2
Score
31
Posts
52
Posts %
2
Score
14
Posts
23
Posts %
1
Score
8
Posts
13
Posts %
Top posts
View all questions and answers
question
6
Does a finite-dimensional algebra have the same length as a regular module when considered as a left module and as a right module?
Apr 29
question
5
How are submodules characterized with respect to the isomorphism of the direct sum of multiple modules?
Dec 5, 2023
question
5
Is the Jacobson radical of the direct product of infinitely many rings the direct product of the Jacobson radicals of each ring?
May 29
question
4
If $M$ is not a finitely generated module over a left Artin ring $\Lambda$, can we still conclude that $M/\operatorname{rad}(M) \neq 0$?
Aug 21
answer
3
If a ring $R$ decomposes as $_R R \simeq P_1 \oplus \cdots \oplus P_n$, can any simple $R$-module be isomorphic to a quotient of some $P_i$?
May 31
question
3
Is there an idempotent e in a ring $R$ such that the functor $T_e$, induced by $e$, is not full?
Feb 23
question
3
If every non-zero left module over a ring contains a simple submodule, does that necessarily mean the ring is a left Artin ring?
Apr 30
question
3
If $R$ is an integral domain, $I$ is an ideal of $R$, and $0\neq f: I \to R$ is an $R$-module homomorphism, can we conclude that $f$ is injective?
Jun 10
question
3
Is a surjective endomorphism of a finitely generated module over a *non-commutative* ring with unity necessarily an isomorphism?
May 3
question
3
An indecomposable module $M$ satisfying $\text{soc}(M) \neq 0$, can we conclude that $\text{soc}(M) \hookrightarrow M$ is an essential extension?
May 31