WEAKLY circle plus-SUPPLEMENTED MODULES AND WEAKLY D2 MODULES


Phan The Hai P. T. H. , KOŞAN M. T. , Truong Cong Quynh T. C. Q.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.57, no.3, pp.691-707, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.4134/bkms.b190420
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.691-707

Abstract

In this paper, we introduce and study the notions of weakly circle plus-supplemented modules, weakly D2 modules and weakly D2-covers. A right R-module M is called weakly circle plus-supplemented if every non-small submodule of M has a supplement that is not essential in M, and module M-R is called weakly D 2 if it satisfies the condition: for every s is an element of S and s not equal 0, if there exists n is an element of N such that s(n) not equal 0 and Im(s(n)) is a direct summand of M, then Ker(sn) is a direct summand of M. The class of weakly circle plus-supplemented-modules and weakly D2 modules contains circle plus-supplemented modules and D2 modules, respectively, and they are equivalent in case M is uniform, and projective, respectively.