We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Generalization of Local Modules.
- Authors
Abed, Majid Mohammed
- Abstract
In this paper we introduce a generalization of local module. The notion of 2-Local module can be considered a new concept (generalization of local modules). Let T be a ring with identity. 2-maximal submodule can define as, any submodule B1 of B is called 2-maximal if (B/B1) is a 2-regular module. 2-Local module means every submodule A of a T-module B where B A is a unique 2-maximal submodule. Almost any unique maximal submodule of a T-module B gives 2-local module. Also, we can present a generalization of local module by, if B is a fully prime module over the ring T and every submodule B1 of a T-module B is a unique almost max-submodule, this means B is a 2-local. Every semi-maximal submodule B1 over chained module B is maximal (2-maximal submodule) and hence B is 2-local module. Some properties and examples of 2-Local module are given. Finally some implications of 3-local module have been presented.
- Subjects
GENERALIZATION; NOETHERIAN rings
- Publication
Iraqi Journal of Science, 2024, Vol 65, Issue 2, p872
- ISSN
0067-2904
- Publication type
Article
- DOI
10.24996/ijs.2024.65.2.24