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Let $R$ be a commutative ring with unity. If $f(x)$ is a zero-divisor polynomial such that $f(x)=c_{f}f_{1}(x)$ with $c_{f}\in R$ and $f_{1}(x)$ is not zero-divisor, then $c_{f}$ is called an annihilating content for $ f(x) $. In this case $Ann(f)=Ann(c_{f})$. We defined EM-rings to be rings with every zero-divisor polynomial having annihilating content. We showed that the class of EM-rings includes integral domains, principal ideal rings, and PP-rings, while it is included in Armendariz rings, and rings having a.c. condition. Some properties of EM-rings are studied and the zero-divisor graphs $\Gamma (R)$ and $\Gamma (R[x])$ are related if $R$ was an EM-ring. Some properties of annihilating contents for polynomials are extended to formal power series rings.
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참고문헌 (19)
참고문헌 신청
Emad ABU OSBA / 2017 / When zero-divisor graphs are divisor graphs / TURKISH JOURNAL OF MATHEMATICS 41:797~807
D.D Anderson / 1985 / The rings R(X) and R〈X〉 / Journal of Algebra 95(1):96~115
D.D. Anderson / 1998 / Armendariz rings and gaussian rings / Communications in Algebra 26(7):2265~2272
D. D. Anderson / 2011 / Irreducible elements in commutative rings with zero-divisors / Houston J. Math 37(3):741~744
. D. Anderson / 1996 / Factorization in commutative rings with zero divi-sors / Rocky Mountain J. Math 26(2):439~480
D.D Anderson / 1985 / The rings R(X) and R〈X〉 / Journal of Algebra 95(1):96~115
D.D. Anderson / 1998 / Armendariz rings and gaussian rings / Communications in Algebra 26(7):2265~2272
D. D. Anderson / 2011 / Irreducible elements in commutative rings with zero-divisors / Houston J. Math 37(3):741~744
. D. Anderson / 1996 / Factorization in commutative rings with zero divi-sors / Rocky Mountain J. Math 26(2):439~480
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