A Note on Modules and Submodules over Polynomial Rings

Authors

Carlos Henrique Tognon, Department of Mathematics, University of Sa ̃o Paulo, ICMC, Sa ̃o Carlos - Sa ̃o Paulo - SP, BrazilFollow
Mansour Lotayif, College of Administrative Sciences, Applied Science University, P.O. Box 5055, East Al-Ekir, Kingdom of BahrainFollow

Author Country (or Countries)

Brazil

Abstract

In this paper, we consider R a commutative ring with identity non-zero and the R-module I(G), which is the edge ideal of a graph simple and finite G, with no isolated vertices. A submodule N of I(G) is called an edge dense submodule if HomR(I(G)/N,ER(I(G))) = 0, where ER(I(G)) is the injective hull of I(G). The R-module I(G) is said to be edge monoform if any nonzero submodule of I(G) is an edge dense submodule. Here in this paper, we presented some results which involve the definition of the module I(G) to be edge monoform.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/150503

Recommended Citation

Henrique Tognon, Carlos and Lotayif, Mansour (2021) "A Note on Modules and Submodules over Polynomial Rings," Applied Mathematics & Information Sciences: Vol. 15: Iss. 5, Article 3.
DOI: http://dx.doi.org/10.18576/amis/150503
Available at: https://digitalcommons.aaru.edu.jo/amis/vol15/iss5/3