Finite-dimensional algebras with smallest resolutions of simple modules
| dc.creator | Jagadeeshan, Shashidhar | |
| dc.creator | Kleiner, Mark | |
| dc.date | 2005-12-30 | |
| dc.date | 2006-08-03 | |
| dc.date.accessioned | 2026-07-07T06:55:54Z | |
| dc.date.available | 2026-07-07T06:55:54Z | |
| dc.description | 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 $Λ$ with the following property. Let $S$ be a simple $Λ$-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. | |
| dc.description | Minor revisions, to appear in Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0512656 | |
| dc.identifier | http://arxiv.org/abs/math/0512656 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106438 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16G10 (Primary); 16G30 (Secondary) | |
| dc.title | Finite-dimensional algebras with smallest resolutions of simple modules | |
| dc.type | text |