Zero-divisor graphs with respect to primal and weakly primal ideals
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We consider zero-divisor graphs with respect to primal, non-primal, weakly prime and weakly primal ideals of a commutative ring R with non-zero identity. We investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of Γ_{I} (R)$ for some ideal I of R. Also we show that the zero-divisor graph with respect to primal ideals commutes by localization.
Abstract
We consider zero-divisor graphs with respect to primal, non-primal, weakly prime and weakly primal ideals of a commutative ring R with non-zero identity. We investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of Γ_{I} (R)$ for some ideal I of R. Also we show that the zero-divisor graph with respect to primal ideals commutes by localization.
참고문헌 (14)
- D. F. Anderson, "Zero-divisor graphs, von Neumann regular rings, and Boolean algebras", J. Pure Appl. Algebra, 180(3), pp.221~241 (2003)
- D. F. Anderson, "The zero-divisor graph of a commutative ring", J. Algebra, 217(2), pp.434~447 (1999)
- D. D. Anderson, "Weakly prime ideals", Houston J. Math., 29(4), pp.831~840 (2003)
- I. Beck, "Coloring of commutative rings", J. Algebra, 116(1), pp.208~226 (1988)
- L. Dancheng, "On ideal-based zero-divisor graphs", Preprint (2006)
- S. Ebrahimi Atani, "Some remarks on primal submodules", Sarajevo Journal of Mathematics, 4(17), pp.181~190 (2008)
- S. Ebrahimi, "On weakly primal ideals (I)", Demonstratio Math., 40(1), pp.23~32 (2007)
- L. Fuchs, "On primal ideals", Proc. Amer. Math. Soc., 1, pp.1~6 (1950)
- J. A. Huckaba, "Commutative Rings with Zero Divisors", Monographs and Textbooks in Pure and Applied Mathematics, 117 (1988), Marcel Dekker, Inc.
- T. G. Lucas, "The diameter of a zero divisor graph", J. Algebra, 301(1), pp.174~193 (2006)
- H. R. Maimani, "Zero-divisor graph with respect to an ideal", Comm. Algebra, 34(3), pp.923~929 (2006)
- S. B. Mulay, "Rings having zero-divisor graphs of small diameter or large girth", Bull. Austral. Math. Soc., 3(3), pp.481~490 (2005)
- S. P. Redmond, "An ideal-based zero-divisor graph of a commutative ring", Comm. Algebra, 31(9), pp.4425~4443 (2003)
- R. Y. Sharp, "Steps in Commutative Algebra", London Mathematical Society Student Texts, 19 (1990), Cambridge University Press