Open AccessG-Rad μ-semiregular modules
Author(s) -
Eman Mohammed,
Waasan Khalid
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1818/1/012172
Subject(s) - generalization , mathematics , combinatorics , ring (chemistry) , identity (music) , discrete mathematics , physics , mathematical analysis , chemistry , organic chemistry , acoustics
Let R be any ring with identity and let M be aunitary left R-module The aim of this paper is to introduce G- R a d µ -semiregular module as a generalization of µ-semiregular module, M is called G- R a d μ -semiregular module,∀ R x in M such that R a d μ ( M ) ≤ R x , there exists a decomposition M=A⊕B, where A is projective submodule of R x and B∩ R x ≪ μ M . On the other hand the notion of R-F-µ-semiregular module as a generalization of F-µ-semiregular module is defined, Let M be an R-module, and let F be a proper submodule of M, M is called R-F-µ-semiregular module, if for each x ∈ M, such that R a d μ ( M ) ≤ F , there exists a projective summand submodule A of R x , such that M=A⊕B, B ≤ M and B∩ R x ≪ μ F. Finally, a condition under which µ-semiregular module be G- R a d μ -semiregular module, is given the basic properties of G- R a d μ -semiregular module. and R-F-µ-semiregular module are proved.