Research Article
Year 2019,
Volume: 40 Issue: 4, 792 - 801, 31.12.2019
Abstract
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.
- [9] Elele A.B. and Ulucak G., 3-Zero-Divisor Hypergraph Regarding an Ideal, 7 th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO), 2017.
- [10] Badawi A., On 2-absorbing Ideals of Commutative Rings, Bull. Austral. Math. Soc.,75 (2007) 417-429.
Year 2019,
Volume: 40 Issue: 4, 792 - 801, 31.12.2019
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.
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.
- [9] Elele A.B. and Ulucak G., 3-Zero-Divisor Hypergraph Regarding an Ideal, 7 th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO), 2017.
- [10] Badawi A., On 2-absorbing Ideals of Commutative Rings, Bull. Austral. Math. Soc.,75 (2007) 417-429.
There are 10 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | December 31, 2019 |
| Submission Date | November 19, 2018 |
| Acceptance Date | October 23, 2019 |
| Published in Issue | Year 2019 Volume: 40 Issue: 4 |