Displaying similar documents to “Graphs based on BCK/BCI-algebras.”

Ideal extensions of graph algebras

Karla Čipková (2006)

Czechoslovak Mathematical Journal

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Let 𝒜 and ℬ be graph algebras. In this paper we present the notion of an ideal in a graph algebra and prove that an ideal extension of 𝒜 by ℬ always exists. We describe (up to isomorphism) all such extensions.

On the connectivity of the annihilating-ideal graphs

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,...

On L-ideal-based L-zero-divisor graphs

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.

An ideal-based zero-divisor graph of direct products of commutative rings

S. Ebrahimi Atani, M. Shajari Kohan, Z. Ebrahimi Sarvandi (2014)

Discussiones Mathematicae - General Algebra and Applications

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In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings.