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S. Ebrahimi Atani, M. Shajari Kohan (2011)
Discussiones Mathematicae - General Algebra and Applications
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In a manner analogous to a commutative ring, the L-ideal-based L-zero-divisor graph of a commutative ring R can be defined as the undirected graph Γ(μ) for some L-ideal μ of R. The basic properties and possible structures of the graph Γ(μ) are studied.
Zoran Pucanović, Zoran Petrović (2011)
Publications de l'Institut Mathématique
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Nader Jafari Rad, Sayyed Heidar Jafari, Shamik Ghosh (2014)
Discussiones Mathematicae - General Algebra and Applications
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In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals of direct product of commutative rings.
S. Ebrahimi Atani, M. Shajari Kohan (2011)
Discussiones Mathematicae - General Algebra and Applications
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L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.
Young Bae Jun, Seok Zun Song (2016)
Discussiones Mathematicae General Algebra and Applications
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The notions of superior subalgebras and (commutative) superior ideals are introduced, and their relations and related properties are investigated. Conditions for a superior ideal to be commutative are provided.
Gary Birkenmeier, Henry E. Heatherly (1990)
Czechoslovak Mathematical Journal
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T. Tamizh Chelvam, K. Selvakumar (2015)
Discussiones Mathematicae - General Algebra and Applications
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Let R be a commutative ring with identity and 𝔸*(R) the set of non-zero ideals with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph 𝔸𝔾(R) with the vertex set 𝔸*(R) and two distinct vertices I₁ and I₂ are adjacent if and only if I₁I₂ = (0). In this paper, we examine the presence of cut vertices and cut sets in the annihilating-ideal graph of a commutative Artinian ring and provide a partial classification of the rings in which they appear. Using this,...
Kleinfeld, Erwin (1993)
Portugaliae mathematica
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Andrzej Prószyński (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove that generating relations between the elements [r] = r²-r of a commutative ring are the following: [r+s] = [r]+[s]+rs[2] and [rs] = r²[s]+s[r].
Petrović, Zoran Z., Moconja, Slavko M. (2008)
Novi Sad Journal of Mathematics
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Bell, Howard E. (2000)
International Journal of Mathematics and Mathematical Sciences
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James R. Mosher (1970)
Compositio Mathematica
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