On essential extensions of direct sums of injective modules

K. I. Beidar, Wen-Fong Ke

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We characterize locally Noetherian modules MR in terms of essential extensions of direct sums of M-injective modules. As a special case (M = R) we obtain that the following conditions are equivalent: (a) R is right Noetherian; (b) any essential extension of the direct sum of any family of injective right R-modules is the direct sum of injective right R-modules; (c) any essential extension of the direct sum of the family (ℰ(Si) | i = 1, 2, ….) of injective hulls of any family (Si | i = 1, 2, ….) of simple right R-modules is the direct sum of injective right R-modules; (d) for any family (Si | i: 1, 2, ….) of simple right R-modules there exists an infinite subset ℐ of natural numbers such that ⊕i∈ℐ, ℰ(Si) is an injective module.

Original languageEnglish
Pages (from-to)120-123
Number of pages4
JournalArchiv der Mathematik
Volume78
Issue number2
DOIs
Publication statusPublished - 2002 Feb 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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