Two characterizations of pure injective modules
| dc.creator | Divaani-Aazar | |
| dc.creator | Esmkhani | |
| dc.creator | Tousi | |
| dc.date | 2005-09-22 | |
| dc.date.accessioned | 2026-07-07T06:18:40Z | |
| dc.date.available | 2026-07-07T06:18:40Z | |
| dc.description | Let $R$ be a commutative ring with identity and $D$ an $R$-module. It is shown that if $D$ is pure injective, then $D$ is isomorphic to a direct summand of the direct product of a family of finitely embedded modules. As a result, it follows that if $R$ is Noetherian, then $D$ is pure injective if and only if $D$ is isomorphic to a direct summand of the direct product of a family of Artinian modules. Moreover, it is proved that $D$ is pure injective if and only if there is a family $\{T_λ\}_{λ\in Λ}$ of $R$-algebras which are finitely presented as $R$-modules, such that $D$ is isomorphic to a direct summand of a module of the form $Π_{λ\in Λ}E_λ$ where for each $λ\in Λ$, $E_λ$ is an injective $T_λ$-module. | |
| dc.description | 8 pages, to appear in Proc. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0509516 | |
| dc.identifier | http://arxiv.org/abs/math/0509516 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94815 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13E10, 13C05 | |
| dc.title | Two characterizations of pure injective modules | |
| dc.type | text |