Open AccessBaer and Quasi-Baer Gamma Modules
Author(s) -
Mubarak Mohammad Kamil,
Saad Abdulkadhim Al-Saadi
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 - 10.1088/1742-6596/1818/1/012017
Subject(s) - endomorphism ring , invertible matrix , mathematics , endomorphism , ring (chemistry) , pure mathematics , class (philosophy) , computer science , chemistry , artificial intelligence , organic chemistry
In this paper we present the concept of (Quasi-) Baer Gamma Module, and as in the class of rings and modules, we provide that : (1) An Γ − ring R is right nonsingular and right (FI-extending) extending if and only if R is (Quasi-) Baer and right cononsingular. (2) An R Γ − Module M is (FI-extending) extending and (FI-K-nonsingular) K-nonsingular if and only if M is (Quasi-) Baer and K-(FI-K-cononsingular) cononsingular. (3) Any direct summand of a (quasi-)Baer R Γ -module is (Quasi-)Baer.(4) The endomorphism Γ − ring S = End ( M ) of (Quasi) Baer R Γ − Module M is (Quasi) Baer.(5) If M be retractable R Γ − Module . Then the endomorphism Γ − ring of M , S , is (Quasi-) Baer if and only if M is a (Quasi-) Baer. Furthermore, other results are introduced.