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ANNIHILATORS IN ONE-SIDED IDEALS GENERATED BY COEFFICIENTS OF ZERO-DIVIDING POLYNOMIALS

이동수|이양|곽태근
대한수학회 (The Korean Mathematical Society)|2014.05|대한수학회지 (Journal of the KMS)|제51권 제3호|pp. 495-507

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참고문헌

키워드

matrix ringpolynomial ringright left-ideal-McCoy ringright McCoy ringcondition (†)Dorroh extension.
주제분류수학

초록

Nielsen and Rege-Chhawchharia called a ring R right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, there exists a nonzero element r ∈ R with f(x)r = 0. Hong et al. called a ring R strongly right McCoy if given nonzero polynomials f(x),g(x) over R with f(x)g(x) = 0, f(x)r = 0 for some nonzero r in the right ideal of R generated by the coefficients of g(x). Subsequently, Kim et al. observed similar conditions on linear polynomials by finding nonzero r’s in various kinds of one-sided ideals generated by coefficients. But almost all results obtained by Kim et al. are concerned with the case of products of linear polynomials. In this paper we examine the nonzero annihilators in the products of general polynomials.

Abstract

Nielsen and Rege-Chhawchharia called a ring R right McCoy if given nonzero polynomials f(x), g(x) over R with f(x)g(x) = 0, there exists a nonzero element r ∈ R with f(x)r = 0. Hong et al. called a ring R strongly right McCoy if given nonzero polynomials f(x),g(x) over R with f(x)g(x) = 0, f(x)r = 0 for some nonzero r in the right ideal of R generated by the coefficients of g(x). Subsequently, Kim et al. observed similar conditions on linear polynomials by finding nonzero r’s in various kinds of one-sided ideals generated by coefficients. But almost all results obtained by Kim et al. are concerned with the case of products of linear polynomials. In this paper we examine the nonzero annihilators in the products of general polynomials.

참고문헌 (26)

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On a generalization of McCoy rings이양, 곽태근, Victor Camillo대한수학회 · 대한수학회지2013 · 제50권 제5호McCoy condition on ideals of coefficients이양, 허찬, 곽태근, 천정수대한수학회 · 대한수학회보2013 · 제50권 제6호Extensions of linearly McCoy ringsJian Cui, Jianlong Chen대한수학회 · 대한수학회보2013 · 제50권 제5호Rings over which polynomial rings are Armendariz and reversible이양, 김정수, 노동현, 노유승, 박경현, 안정호, 이순지, 이영선, 이정렬, 이창익, 정원석, 최민정, 최시라강원경기수학회 · 한국수학논문집2012 · 제20권 제3호On NI and quasi-NI rings이양, 김동화, 윤상조, 이성익강원경기수학회 · 한국수학논문집2016 · 제24권 제3호A STRUCTURE ON COEFFICIENTS OF NILPOTENT POLYNOMIALS이양, 류성주, 전영철대한수학회 · 대한수학회지2010 · 제47권 제4호

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