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On generalized zero-divisor graphs of a non-commutative ring with respect to an ideal
- Source :
- Asian-European Journal of Mathematics. 15
- Publication Year :
- 2021
- Publisher :
- World Scientific Pub Co Pte Ltd, 2021.
-
Abstract
- Let R be a non-commutative ring, and I be an ideal of R. In this paper, we generalize the definition of the zero-divisor graph of R with respect to I, and define several generalized zero-divisor graphs of R with respect to I. In this paper, we investigate the ring-theoretic properties of R and the graph-theoretic properties of all the generalized zero-divisor graphs. We study some basic properties of these generalized zero-divisor graphs related to the connectedness, the diameter and the girth. We also investigate some properties of these generalized zero-divisor graphs with respect to primal ideals.
- Subjects :
- Ring (mathematics)
Computer Science::Information Retrieval
General Mathematics
Astrophysics::Instrumentation and Methods for Astrophysics
Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)
Commutative ring
Girth (graph theory)
Graph
Combinatorics
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
Computer Science::General Literature
Ideal (ring theory)
ComputingMilieux_MISCELLANEOUS
Zero divisor
MathematicsofComputing_DISCRETEMATHEMATICS
Mathematics
Subjects
Details
- ISSN :
- 17937183 and 17935571
- Volume :
- 15
- Database :
- OpenAIRE
- Journal :
- Asian-European Journal of Mathematics
- Accession number :
- edsair.doi...........cd6e7e72017973c6ed0a99ac01fe9620