Algebraic Compactness OF $\prod M_α/ \oplus M_α$
| dc.creator | Dimitric, Radoslav | |
| dc.date | 2007-08-20 | |
| dc.date.accessioned | 2026-07-07T08:24:21Z | |
| dc.date.available | 2026-07-07T08:24:21Z | |
| dc.description | In this note, we are working within the category $\rmod$ of (unitary, left) $R$-modules, where $R$ is a {\bf countable} ring. It is well known (see e.g. Kiełpiński & Simson [5], Theorem 2.2) that the latter condition implies that the (left) pure global dimension of $R$ is at most 1. Given an infinite index set $A$, and a family $M_\al\in\rmod$, $\al\in A$ we are concerned with the conditions as to when the $R$-module $$\prod/\coprod=\prod_{\al\in A}M_\al/\bigoplus_{\al\in A}M_\al$$ is or is not algebraically compact. There are a number of special results regarding this question and this note is meant to be an addition to and a generalization of the set of these results. Whether the module in the title is algebraically compact or not depends on the numbers of algebraically compact and non-compact modules among the components $M_\al$. | |
| dc.identifier | https://arxiv.org/abs/0708.2569 | |
| dc.identifier | http://arxiv.org/abs/0708.2569 | |
| dc.identifier | Internat. J. Pure Applied Math, 10(2004), No.3, 203-206 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136312 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Group Theory | |
| dc.subject | Logic | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16D10, 16D80, 13C13 | |
| dc.title | Algebraic Compactness OF $\prod M_α/ \oplus M_α$ | |
| dc.type | text |