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2011 | 31 | 2 | 159-174
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L-zero-divisor graphs of direct products of L-commutative rings

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EN
Abstrakty
EN
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.
Twórcy
  • Faculty of Mathematical Science, University of Guilan, P.O. Box 1914, Rasht, Iran
  • Faculty of Mathematical Science, University of Guilan, P.O. Box 1914, Rasht, Iran
Bibliografia
  • [1] D.F. Anderson and P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), 434-447. doi: 10.1006/jabr.1998.7840
  • [2] M. Axtell, J. Stickles and J. Warfel, Zero-divisor graphs of direct products of commutative rings, Houston J. of Math. 22 (2006), 985-994.
  • [3] D.F. Anderson, M.C. Axtell and J.A. Stickles, Zero-divisor graphs in commutative rings, in: Commutative Algebra, Noetherian and non-Noetherian Perspectives (M. Fontana, S.-E. Kabbaj, B. Olberding, I. Swanson, Eds), Springer-Verlag, New York, 2.11, 23-45.
  • [4] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), 208-226. doi: 10.1016/0021-8693(88)90202-5
  • [5] S. Ebrahimi Atani and M. Shajari Kohan, On L-ideal-based L-zero-divisor graphs, Discuss. Math. General Algebra and Applications, to appear.
  • [6] I. Goguen, L-fuzzy sets, J. Math. Appl. 18 (1967), 145-174.
  • [7] W.J. Liu, Operations on fuzzy ideals, Fuzzy Sets and Systems, 11 (1983), 31-41.
  • [8] L. Martinez, Prime and primary L-fuzzy ideals of L-fuzzy rings, Fuzzy Sets and Systems 101 (1999), 489-494. doi: 10.1016/S0165-0114(97)00114-0
  • [9] J.N. Mordeson and D.S. Malik, Fuzzy Commutative Algebra, J. World Scientific Publishing, Singapore, 1998.
  • [10] S.B. Mulay, Cycles and symmetries of zero-divisors, Comm. Algebra 30 (7) (2002), 3533-3558. doi: 10.1081/AGB-120004502
  • [11] A. Rosenfeld, Fuzzy groups, J. Math. Appl. 35 (1971), 512-517.
  • [12] A. Rosenfeld, In fuzzy sets and their applications to Cognitive and Decision Processes, Zadeh L.A, Fu K.S., Shimura M., Eds, Academic Press, New York (1975), 77-95.
  • [13] R.T Yeh and S.Y. Banh, Fuzzy relations, fuzzy graphs and their applications to clustering analysis, in: Fuzzy sets and their applications to Cognitive and Decision Processes, Zadeh L.A, Fu K.S., Shimura M., Eds, Academic Press, New York (1975), 125-149.
  • [14] L.A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1180
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