On submodules of monomial ideal
DOI:
https://doi.org/10.17268/sel.mat.2026.01.10Keywords:
2-absorbing submodule, 2-absorbing primary submodule, weakly 2-absorbing primary submodule, edge ideal of a graphAbstract
In this paper we introduce the notion of weakly 2-absorbing primary submodules of modules and investigate this concept when the ambient module is the edge ideal of a finite simple graph without isolated vertices. Several structural properties concerning quotients, localization and related module constructions are established.
References
[1] Alilooee A, Banerjee A. Powers of edge ideals of regularity three bipartite graphs. J Commut Algebra. 2017; 9:441–454.
[2] Anderson DF, Badawi A. On n-absorbing ideals of commutative rings. Comm Algebra. 2011; 39:1646–1672.
[3] Anderson DD, Smith E. Weakly prime ideals. Houston J Math. 2003; 29:831–840.
[4] Atani SE, Farzalipour F. On weakly primary ideal. Georgian Math J. 2005; 12:423–429.
[5] Atiyah MF, Macdonald IG. Introduction to Commutative Algebra. Reading (MA): Addison-Wesley; 1969.
[6] Badawi A. On 2-absorbing ideals of commutative rings. Bull Aust Math Soc. 2007; 75:417-429.
[7] Badawi A, Darani AY. On weakly 2-absorbing ideals of commutative rings. Houston J Math. Forthcoming.
[8] Badawi A, Tekir U, Yetkin E. On 2-absorbing primary ideals in commutative rings. Bull Korean Math Soc. 2014; 51:1163-1173.
[9] Rotman JJ. An Introduction to Homological Algebra. New York: Academic Press; 1979.
[10] Simis A, Vasconcelos WV, Villarreal RH. The integral closure of subrings associated to graphs. J Algebra. 1998; 199:281–289.
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