Projective dimension is a lattice invariant
| dc.creator | Osofsky, Barbara L. | |
| dc.date | 2000-07-14 | |
| dc.date.accessioned | 2026-07-07T04:36:23Z | |
| dc.date.available | 2026-07-07T04:36:23Z | |
| dc.description | We show that, for a free abelian group $G$ and prime power $p^ν$, every direct sum decomposition of the group $G/p^νG$ lifts to a direct sum decomposition of $G$. This is the key result we use to show that, if $R$ is a commutative von Neumann regular ring, and $\mathcal{E}$ a set of idempotents in $R$, then the projective dimension of the ideal $\mathcal{E} R$ as an $R$-module is the same as the projective dimension of the ideal $\mathcal{EB}$, where $\mathcal{B}$ is the boolean algebra generated by $\mathcal{E} \cup \{1\}$. This answers a thirty year old open question of R. Wiegand. The proof is based on gaussian elimination on an $ω\times ω$ matrix, with adaptations enabling one to pass from the integers modulo $p^ν$ to the integers. | |
| dc.description | LaTex. 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0007091 | |
| dc.identifier | http://arxiv.org/abs/math/0007091 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59577 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Group Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 13D05, 20K99 (Primary) 06E20 (Secondary) | |
| dc.title | Projective dimension is a lattice invariant | |
| dc.type | text |