On En- Prime Compactly Packed Acts over Monoid
DOI:
https://doi.org/10.21123/bsj.2024.11424Keywords:
En- Prime subacts, En-prime submodules, En-Pure subacts, En-prime compactly packed S-Act, Multiplication S-actAbstract
This work studies the concept of En-prime compactly packed modules. Some properties and characterizations have been studied. Put ₩ is an Я-module and every submodule is En-pure , then ₩ is if and only if each proper submodule of ₩ is cyclic, If ₩ is ₩ which has at least one maximal submodule then ₩ satisfies the ACC on En-p-radical submodule. The generalization of this idea has been given for S-Acts. if for each family of En-prime subact of Д with Ѫ , for some . An S-Act Д is , if every subact is . Various properties of modules and S-Acts have been studied, like, ₩ is an R-module and every submodule is En-pure, then ₩ is if and only if each proper submodule of ₩ is cyclic. The general is, if Д is S-Act which has at least one maximal subact then Д satisfies the ACC on En-p-radical subact.and suppose that Д is an S-Act. If the CST is satisfied for Д, then , and prove that, If Д is a multiplication S-Act that satisfies the ACC on En-p- radical subact, then for every proper subact Ѫ of Д there exists a finite number of minimal En-prime subact of Ѫ. Let f: be an epimorphism. If is then so is . The converse is true when Д is finitely generated or (multiplication) S-Act and .
Received 21/04/2024
Revised 04/10/2024
Accepted 06/10/2024
Published Online First 20/11/2024
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Copyright (c) 2024 Samira Naji Kadhim, Uhood S. AL-Hussani, Muna Jasim
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