When Some Complement of an EC-Submodule is a Direct Summand

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CELEP YÜCEL C., TERCAN A.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.50, no.1, pp.101-107, 2010 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 1
  • Publication Date: 2010
  • Doi Number: 10.5666/kmj.2010.50.1.101
  • Journal Name: KYUNGPOOK MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.101-107
  • Hacettepe University Affiliated: Yes

Abstract

A module M is said to satisfy the EC11 condition if every ec-submodule of M has a complement which is a direct summand. We show that for a multiplication module over a commutative ring the EC11 and P-extending conditions are equivalent. It is shown that the EC11 property is not inherited by direct summands. Moreover, we prove that if M is an EC11-module where SocM is an ec-submodule, then it is a direct sum of a module with essential socle and a module with zero socle. An example is given to show that the reverse of the last result does not hold.