Classical 2-Absorbing Submodules of Modules over Commutative Rings

EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, cilt.8, sa.3, ss.417-430, 2015 (ESCI İndekslerine Giren Dergi)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 8 Konu: 3
• Basım Tarihi: 2015
• Dergi Adı: EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
• Sayfa Sayıları: ss.417-430

Özet

In this article, all rings are commutative with nonzero identity. Let M be an R- module. A proper submodule N of M is called a classical prime submodule, if for each m is an element of M and elements a, b is an element of R, abm is an element of N implies that am is an element of N or bm is an element of N. We introduce the concept of " classical 2- absorbing submodules" as a generalization of "classical prime submodules". We say that a proper submodule N of M is a classical 2-absorbing submodule if whenever a, b, c is an element of R and m is an element of M with abcm is an element of N, then abm is an element of N or acm is an element of N or bcm is an element of N.