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BibTex RIS Kaynak Göster

Yıl 2019, Cilt: 40 Sayı: 4, 792 - 801, 31.12.2019

Gülşen Ulucak

https://doi.org/10.17776/csj.485085

Öz

Kaynakça

  • [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.

3-Zero-Divisor Hypergraph with Respect to an Element in Multiplicative Lattice

Yıl 2019, Cilt: 40 Sayı: 4, 792 - 801, 31.12.2019

Gülşen Ulucak

https://doi.org/10.17776/csj.485085

Öz

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.

Anahtar Kelimeler

3-Zero-Divisor Hypergraph Complete n-partite Hypergraph.

Kaynakça

  • [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.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Natural Sciences
Yazarlar

Gülşen Ulucak 0000-0001-6690-6671

Yayımlanma Tarihi 31 Aralık 2019
Gönderilme Tarihi 19 Kasım 2018
Kabul Tarihi 23 Ekim 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 40 Sayı: 4

Kaynak Göster

APA Ulucak, G. (2019). 3-Zero-Divisor Hypergraph with Respect to an Element in Multiplicative Lattice. Cumhuriyet Science Journal, 40(4), 792-801. https://doi.org/10.17776/csj.485085