L-zero-divisor graphs of direct products of L-commutative rings

S. Ebrahimi Atani; M. Shajari Kohan

Discussiones Mathematicae - General Algebra and Applications (2011)

  • Volume: 31, Issue: 2, page 159-174
  • ISSN: 1509-9415

Abstract

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L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.

How to cite

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S. Ebrahimi Atani, and M. Shajari Kohan. "L-zero-divisor graphs of direct products of L-commutative rings." Discussiones Mathematicae - General Algebra and Applications 31.2 (2011): 159-174. <http://eudml.org/doc/276609>.

@article{S2011,
abstract = {L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.},
author = {S. Ebrahimi Atani, M. Shajari Kohan},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {μ-zero-divisor; L-zero-divisor graph; μ-diameter; μ-girth; finite direct products; -zero-divisor; -zero-divisor graph; -diameter; -girth},
language = {eng},
number = {2},
pages = {159-174},
title = {L-zero-divisor graphs of direct products of L-commutative rings},
url = {http://eudml.org/doc/276609},
volume = {31},
year = {2011},
}

TY - JOUR
AU - S. Ebrahimi Atani
AU - M. Shajari Kohan
TI - L-zero-divisor graphs of direct products of L-commutative rings
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2011
VL - 31
IS - 2
SP - 159
EP - 174
AB - L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.
LA - eng
KW - μ-zero-divisor; L-zero-divisor graph; μ-diameter; μ-girth; finite direct products; -zero-divisor; -zero-divisor graph; -diameter; -girth
UR - http://eudml.org/doc/276609
ER -

References

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  10. [10] S.B. Mulay, Cycles and symmetries of zero-divisors, Comm. Algebra 30 (7) (2002), 3533-3558. doi: 10.1081/AGB-120004502 Zbl1087.13500
  11. [11] A. Rosenfeld, Fuzzy groups, J. Math. Appl. 35 (1971), 512-517. Zbl0194.05501
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