Modules with Chain Conditions on S-Closed Submodules | Zendy

Raoori Majeed Mohammed | Zendy

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Modules with Chain Conditions on S-Closed Submodules

Author(s) -

Raoori Majeed Mohammed

Publication year - 2017

Publication title -

ibn al- haitham journal for pure and applied science

Language(s) - English

Resource type - Journals

eISSN - 2521-3407

pISSN - 1609-4042

DOI - 10.30526/30.3.1618

Subject(s) - unitary state , commutative ring , mathematics , chain (unit) , extension (predicate logic) , ring (chemistry) , identity (music) , pure mathematics , commutative property , combinatorics , discrete mathematics , topology (electrical circuits) , arithmetic , computer science , physics , programming language , law , chemistry , quantum mechanics , organic chemistry , political science , acoustics

Let L be a commutative ring with identity and let W be a unitary left Lmodule. A submodule D of an Lmodule W is called sclosed submodule denoted by D ≤sc W, if D has no proper sessential extension in W, that is , whenever D ≤ W such that D ≤se H≤ W, then D = H. In this paper, we study modules which satisfies the ascending chain conditions (ACC) and descending chain conditions (DCC) on this kind of submodules.

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