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WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED

Yıl 2017, , 198 - 216, 17.01.2017
https://doi.org/10.24330/ieja.296332

Öz

Let R be a commutative ring with nonzero identity and I a proper
ideal of R. The ideal-based zero-divisor graph of R with respect to the ideal
I, denoted by ΓI (R), is the graph on vertices {x ∈ R \ I | xy ∈ I for some
y ∈ R\I}, where distinct vertices x and y are adjacent if and only if xy ∈ I. In
this paper, we give a complete classification of when an ideal-based zero-divisor
graph of a commutative ring is complemented or uniquely complemented based
on the total quotient ring of R/I.

Kaynakça

  • [1] D. F. Anderson, R. Levy and J. Shapiro, Zero-divisor graphs, von Neumann
  • regular rings, and Boolean algebras, J. Pure Appl. Algebra, 180(3) (2003), 221–241.
  • [2] D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative
  • ring, J. Algebra, 217(2) (1999), 434–447.
  • [3] I. Beck, Coloring of commutative rings, J. Algebra, 116(1) (1988), 208–226.
  • [4] R. Levy and J. Shapiro, The zero-divisor graph of von Neumann regular rings,
  • Comm. Algebra, 30(2) (2002), 745–750.
  • [5] P. S. Livingston, Structure in Zero-Divisor Graphs of Commuative Rings, Masters
  • Thesis, Univeristy of Tennessee, Knoxville, TN, 1997
  • [6] S. P. Redmond, Generalizations of the Zero-Divisor Graph of a Ring, Ph.D.
  • Thesis, The University of Tennessee, Knoxville, TN, 2001.
  • [7] S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring,
  • Comm. Algebra, 31(9) (2003), 4425–4443.
  • [8] J. G. Smith, Properties of Ideal-Based Zero-Divisor Graphs of Commutative
  • Rings, Ph.D. Thesis, The Univeristy of Tennessee, Knoxville, TN, 2014.
Yıl 2017, , 198 - 216, 17.01.2017
https://doi.org/10.24330/ieja.296332

Öz

Kaynakça

  • [1] D. F. Anderson, R. Levy and J. Shapiro, Zero-divisor graphs, von Neumann
  • regular rings, and Boolean algebras, J. Pure Appl. Algebra, 180(3) (2003), 221–241.
  • [2] D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative
  • ring, J. Algebra, 217(2) (1999), 434–447.
  • [3] I. Beck, Coloring of commutative rings, J. Algebra, 116(1) (1988), 208–226.
  • [4] R. Levy and J. Shapiro, The zero-divisor graph of von Neumann regular rings,
  • Comm. Algebra, 30(2) (2002), 745–750.
  • [5] P. S. Livingston, Structure in Zero-Divisor Graphs of Commuative Rings, Masters
  • Thesis, Univeristy of Tennessee, Knoxville, TN, 1997
  • [6] S. P. Redmond, Generalizations of the Zero-Divisor Graph of a Ring, Ph.D.
  • Thesis, The University of Tennessee, Knoxville, TN, 2001.
  • [7] S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring,
  • Comm. Algebra, 31(9) (2003), 4425–4443.
  • [8] J. G. Smith, Properties of Ideal-Based Zero-Divisor Graphs of Commutative
  • Rings, Ph.D. Thesis, The Univeristy of Tennessee, Knoxville, TN, 2014.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Konular Matematik
Bölüm Makaleler
Yazarlar

Jesse Gerald Smith Jr Bu kişi benim

Yayımlanma Tarihi 17 Ocak 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Smith Jr, J. G. (2017). WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED. International Electronic Journal of Algebra, 21(21), 198-216. https://doi.org/10.24330/ieja.296332
AMA Smith Jr JG. WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED. IEJA. Ocak 2017;21(21):198-216. doi:10.24330/ieja.296332
Chicago Smith Jr, Jesse Gerald. “WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED”. International Electronic Journal of Algebra 21, sy. 21 (Ocak 2017): 198-216. https://doi.org/10.24330/ieja.296332.
EndNote Smith Jr JG (01 Ocak 2017) WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED. International Electronic Journal of Algebra 21 21 198–216.
IEEE J. G. Smith Jr, “WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED”, IEJA, c. 21, sy. 21, ss. 198–216, 2017, doi: 10.24330/ieja.296332.
ISNAD Smith Jr, Jesse Gerald. “WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED”. International Electronic Journal of Algebra 21/21 (Ocak 2017), 198-216. https://doi.org/10.24330/ieja.296332.
JAMA Smith Jr JG. WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED. IEJA. 2017;21:198–216.
MLA Smith Jr, Jesse Gerald. “WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED”. International Electronic Journal of Algebra, c. 21, sy. 21, 2017, ss. 198-16, doi:10.24330/ieja.296332.
Vancouver Smith Jr JG. WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED. IEJA. 2017;21(21):198-216.