Injective module and C1-module

Talak, Abdulsalam F.; Abed, Majid Mohammed

doi:10.1063/5.0066842

Cited by 2 publications

(3 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since S=EndT(B) is semi-simple ring, then S is a semi-simple ring. From B is a faithful multiplication module and from Theorem 2.44 in [17], we get B is a f.generated multiplication module over T (B1 is f. generated submodule). Hence B1 is 3-max-submodule Now, according to the above, we present some important results about: 1.…”

Section: Discussionmentioning

confidence: 94%

“…If B is a semi-simple module over semi-simple ring S=EndR(B), then 3-maximal submodule. Proof: Assume that B is a semi-simple over S. But A=JB (multiplication module) over T. From Theorem 2.43 in [17], B is a faithful module. Since S=EndT(B) is semi-simple ring, then S is a semi-simple ring.…”

Section: Discussionmentioning

confidence: 99%

“…A module B is multiplication if, A=JB where J is an ideal in T and A submodule of B [15]. From ( [16], [17]), faithful multiplication module and Injective module.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalization of Local Modules

Abed

2024

Iraqi Journal of Science

View full text Add to dashboard Cite

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 is a unique 2-maximal submodule. Almost any unique maximal submodule of a T-module gives 2-local module. Also, we can present a generalization of local module by, if is a fully prime module over the ring and every submodule B1 of a T-module B is a unique almost max-submodule, this means is a 2-local. Every semi-maximal submodule over chained module is maximal (2-maximal submodule) and hence is 2-local module. Some properties and examples of 2-Local module are given. Finally some implications of 3-local module have been presented.

show abstract

Section: Discussionmentioning

confidence: 94%

Section: Discussionmentioning

confidence: 99%