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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.
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참고문헌 (14)
참고문헌 신청
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math. 29 (4) : 831 ~ 840
D. F. Anderson / 1999 / The zero-divisor graph of a commutative ring / J. Algebra 217 (2) : 434 ~ 447
D. F. Anderson / 2003 / Zero-divisor graphs, von Neumann regular rings, and Boolean algebras / J. Pure Appl. Algebra 180 (3) : 221 ~ 241
H. R. Maimani / 2006 / Zero-divisor graph with respect to an ideal / Comm. Algebra 34 (3) : 923 ~ 929
I. Beck / 1988 / Coloring of commutative rings / J. Algebra 116 (1) : 208 ~ 226
D. F. Anderson / 1999 / The zero-divisor graph of a commutative ring / J. Algebra 217 (2) : 434 ~ 447
D. F. Anderson / 2003 / Zero-divisor graphs, von Neumann regular rings, and Boolean algebras / J. Pure Appl. Algebra 180 (3) : 221 ~ 241
H. R. Maimani / 2006 / Zero-divisor graph with respect to an ideal / Comm. Algebra 34 (3) : 923 ~ 929
I. Beck / 1988 / Coloring of commutative rings / J. Algebra 116 (1) : 208 ~ 226
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