Open Accesss-Compressible and s-Prime Modules
Author(s) -
Asaad M. A. Alhossaini
Publication year - 2022
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2022.63.3.25
Subject(s) - prime (order theory) , mathematics , compressibility , identity (music) , ring (chemistry) , pure mathematics , discrete mathematics , combinatorics , physics , mechanics , acoustics , chemistry , organic chemistry
Let R be a ring with identity and Ą a left R-module. In this article, we introduce new generalizations of compressible and prime modules, namely s-compressible module and s-prime module. An R-module A is s-compressible if for any nonzero submodule B of A there exists a small f in HomR(A, B). An R-module A is s-prime if for any submodule B of A, annR (B) A is small in A. These concepts and related concepts are studied in as well as many results consist properties and characterizations are obtained.