Far East Journal of Applied Mathematics

The Far East Journal of Applied Mathematics publishes original research papers and survey articles in applied mathematics, covering topics such as nonlinear dynamics, approximation theory, and mathematical modeling. It encourages papers focusing on algorithm development.

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ON AN $\omega$-EDGE IDEAL OF A SIMPLE GRAPH

Authors

  • C. H. Tognon

Keywords:

$\omega$-edge ideal, semisimple modules, edge coatomic, edge reduced, edge ideal of a graph

DOI:

https://doi.org/10.17654/0972096023013

Abstract

Considering a commutative ring $R$ with non-zero identity and the $R$-module $I(G)$,  which is the edge ideal of a finite simple graph $G$, with no isolated vertex, we introduce the notion of an $\omega$-edge ideal, which is a module. We establish some results which involve the sum of $\omega$-edge ideals.

Received: April 24, 2023
Revised: September 8, 2023
Accepted: September 15, 2023

 

References

A. Alilooee and A. Banerjee, Powers of edge ideals of regularity three bipartite graphs, Journal of Commutative Algebra 9 (2017), 441-454.

M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, University of Oxford, 1969.

J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting modules, Supplements and Projectivity in Module Theory, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2006.

F. Kasch, Modules and rings, London Mathematical Society Monographs, Academic Press, London, Vol. 17, 1982.

H. Matsumura, Commutative ring theory, translated from the Japanese by M. Reid, 2nd ed., Cambridge Studies in Advanced Mathematics, 8, Cambridge University Press, Cambridge, 1989.

J. J. Rotman, An Introduction to Homological Algebra, University of Illinois, Urbana, Academic Press, 1979.

A. Simis, W. V. Vasconcelos and R. H. Villarreal, The integral closure of subrings associated to graphs, J. Algebra 199 (1998), 281-289.

H. Zöschinger, Komplementierte moduln über Dedekindringen, J. Algebra 29 (1974), 42-56.

R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.

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Published

2023-10-12

Issue

Vol. 116 No. 3 (2023)

Section

Articles

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How to Cite

ON AN $\omega$-EDGE IDEAL OF A SIMPLE GRAPH. (2023). Far East Journal of Applied Mathematics, 116(3), 237-247. https://doi.org/10.17654/0972096023013

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