Finite-dimensional algebras with smallest resolutions of simple modules

Details Finite-dimensional algebras with smallest resolutions of simple modules Finite-dimensional algebras with smallest resolutions of simple modules

2005-12-30

arxiv.org/abs/math/0512656v2

Mathematics

Representation Theory

Minor revisions, to appear in Journal of Algebra

Scientific paper

Let $X$ be a finitely generated left module over a left artinian ring $R$, and let $p(X)=\{l_i\}$ be the infinite sequence of nonnegative integers where $l_i$ is the length of the $i$-th term of the minimal projective resolution of $X$. We introduce a preorder relation $\le$ on the set $\{p(X)\}$ and characterize the elementary finite-dimensional algebras $\Lambda$ with the following property. Let $S$ be a simple $\Lambda$-module, and let $T$ be a finitely generated module over an arbitrary left artinian ring $R$. If the projective dimension of $S$ does not exceed the projective dimension of $T$, then $p(S)\le p(T)$. We characterize the indicated algebras by quivers with relations.

Affiliated with

Also associated with

No associations

Rating

Finite-dimensional algebras with smallest resolutions of simple modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finite-dimensional algebras with smallest resolutions of simple modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite-dimensional algebras with smallest resolutions of simple modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-398882