Open Accessstrongly N-extending Strongly N-extending Modules
Author(s) -
Darya jabar,
Saad Abdulkadhim Al-Saad
Publication year - 2021
Publication title -
mağallaẗ al-qādisiyyaaẗ li-l-ʻulūm al-ṣirfaẗ
Language(s) - English
Resource type - Journals
eISSN - 2411-3514
pISSN - 1997-2490
DOI - 10.29350/qjps.2021.26.4.1350
Subject(s) - mathematics , extension (predicate logic) , pure mathematics , invariant (physics) , algebra over a field , computer science , programming language , mathematical physics
Relative extending modules and relative (quasi-)continuous modules were introduced and studied by Oshiro as a generalizations of extending modules and (quasi-) continuous respectively. On other hand, Oshiro, Rizvi and Permouth introduced N-extending and N-(quasi-) continuous modules depending where N and M are modules. is closed under submodules, essential extension and isomorphic image. A module M is N-extending if for each submodule A , there is a direct summand B of M such that A is essential in B. Moreover, a module M is strongly extending if every submodule is essential in a stable (equivalently, fully invariant) direct summand of M.
In this paper, we introduce and study classes of modules which are proper stronger than that of N-extending modules and N-(quasi-)continuous modules. Many characterizations and properties of these classes are given.