When Some Complement of an EC-Submodule is a Direct Summand
KYUNGPOOK MATHEMATICAL JOURNAL, cilt.50, sa.1, ss.101-107, 2010 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 50 Sayı: 1
- Basım Tarihi: 2010
- Doi Numarası: 10.5666/kmj.2010.50.1.101
- Dergi Adı: KYUNGPOOK MATHEMATICAL JOURNAL
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.101-107
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Hacettepe Üniversitesi Adresli: Evet
Özet
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.