ON COMULTIPLICATION AND R-MULTIPLICATION MODULES

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NIKSERESHT A.; SHARIF h.

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Journal Paper

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Journal: Journal of Algebraic Systems Year:2014 | Volume:2 | Issue:1 Page(s): 1-19

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Title

ON COMULTIPLICATION AND R-MULTIPLICATION MODULES

Author(s)

NIKSERESHT A. | SHARIF h. | Issue Writer Certificate

Keywords

Comultiplication Module

Multiplication Module

Comultiplication Mod

ule

Abstract

We state several conditions under which comultiplica-tion and weak Multiplication Module/fa?page=1&sort=1&ftyp=all&fgrp=all&fyrs=all" target="_blank">CoMultiplication Modules are cyclic and study strong Multiplication Module/fa?page=1&sort=1&ftyp=all&fgrp=all&fyrs=all" target="_blank">CoMultiplication Modules and comultiplication rings. In particu-lar, we will show that every faithful weak Multiplication Module/fa?page=1&sort=1&ftyp=all&fgrp=all&fyrs=all" target="_blank">CoMultiplication Module having a maximal submodule over a reduced ring with a nite in-decomposable decomposition is cyclic. Also we show that if M is an strong comultiplication R-module, then R is semilocal and M is nitely cogenerated. Furthermore, we de ne an R-module M to be p-comultiplication, if every nontrivial submodule of M is the annihilator of some prime ideal of R containing the annihila-tor of M and give a characterization of all cyclic p-Multiplication Module/fa?page=1&sort=1&ftyp=all&fgrp=all&fyrs=all" target="_blank">CoMultiplication Modules. Moreover, we prove that every p-Multiplication Module/fa?page=1&sort=1&ftyp=all&fgrp=all&fyrs=all" target="_blank">CoMultiplication Module which is not cyclic, has no maximal submodule and its annihilator is not prime. Also we give an example of a module over a Dedekind domain which is not weak comultiplication, but all of whose local-izations at prime ideals are comultiplication and hence serves as a counterexample to [11, Proposition 2. 3] and [12, Proposition 2. 4].

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APA: Copy

NIKSERESHT, A., & SHARIF, h.. (2014). ON COMULTIPLICATION AND R-MULTIPLICATION MODULES. JOURNAL OF ALGEBRAIC SYSTEMS, 2(1), 1-19. SID. https://sid.ir/paper/718140/en

Vancouver: Copy

NIKSERESHT A., SHARIF h.. ON COMULTIPLICATION AND R-MULTIPLICATION MODULES. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2014;2(1):1-19. Available from: https://sid.ir/paper/718140/en

IEEE: Copy

A. NIKSERESHT, and h. SHARIF, “ON COMULTIPLICATION AND R-MULTIPLICATION MODULES,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 2, no. 1, pp. 1–19, 2014, [Online]. Available: https://sid.ir/paper/718140/en

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