3-Zero-Divisor Hypergraph with Respect to an Element in Multiplicative Lattice
Abstract
Let be a multiplicative lattice and be a proper element of . We introduce the 3-zero-divisor hypergraph of with respect to which is a hypergraph whose vertices are elements of the set where distinct vertices and are adjacent, that is, is a hyperedge if and only if . Throughout this paper, the hypergraph is denoted by We investigate many properties of the hypergraph over a multiplicative lattice. Moreover, we find a lower bound of diameter of and obtain that is connected.
Keywords
References
- [1] Jayaram C. and Johnson E.W., Some Results on Almost Principal Element Lattices, Period. Math. Hungar, 31 (1995) 33-42.
- [2] Anderson D.D., Abstract Commutative Ideal Theory without Chain Condition, Algebra Universalis, 6 (1976) 131-145.
- [3] Anderson D.F. and Livingston P.S., The Zero Divisor of a Commutative Ring, J. of Algebra, (1999) 434-447.
- [4] Dilworth R.P., Abstract Commutative Ideal Theory, Pacific Journal of Mathematics 12 (1962) 481-498.
- [5] Eslahchi Ch. and Rahimi A.M., The k-Zero-Divisor Hypergraph of a Commutative Ring, Int. J. Math. Math. Sci. Art. 50875 (2007) 15.
- [6] Beck I., Coloring of Commutative Rings, J. of Algebra, (1988) 208-226.
- [7] Selvakumar K. and Ramanathana V., Classification of non-Local Rings with Genus One 3-zero-divisor Hypergraphs, Comm. Algebra, (2016) 275-284.
- [8] Akbari S. and Mohammadian A., On the Zero-Divisor Graph of a Commutative Ring, J. Algebra, (2004) 847-855.
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Authors
Gülşen Ulucak
*
0000-0001-6690-6671
Türkiye
Publication Date
December 31, 2019
Submission Date
November 19, 2018
Acceptance Date
October 23, 2019
Published in Issue
Year 1970 Volume: 40 Number: 4