Open AccessSemi-T-Hollow Modules and Semi-T-Lifting Modules
Author(s) -
Alaa A. Elewi
Publication year - 2021
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.152
H-Index - 4
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2021.62.7.24
Subject(s) - mathematics , unitary state , associative property , identity (music) , ring (chemistry) , zero (linguistics) , pure mathematics , discrete mathematics , combinatorics , topology (electrical circuits) , arithmetic , physics , linguistics , chemistry , philosophy , organic chemistry , political science , acoustics , law
Let be an associative ring with identity and let be a unitary left -module. Let be a non-zero submodule of .We say that is a semi- - hollow module if for every submodule of such that is a semi- - small submodule ( ). In addition, we say that is a semi- - lifting module if for every submodule of , there exists a direct summand of and such that
The main purpose of this work was to develop the properties of these classes of module.