On skew polynomials over Ikeda-Nakayama rings

Abstract A ring R is called a left Ikeda-Nakayama ring (left IN-ring) if the right annihilator of the intersection of any two left ideals is the sum of the two right annihilators. Also a ring R is called a right SA-ring if the sum of right annihilators of two ideals is a right annihilator of an ideal of R. In this paper for a compatible endomorphism α of R, we show that: (i) If is a left IN-ring, then R is an Armendariz left IN-ring. (ii) If R is a reduced left IN-ring with finitely many minimal prime ideals, then is a left IN-ring. (iii) is a right SA-ring, if and only if R is a quasi-Armendariz right SA-ring. We give a class of non-reduced rings R such that is left IN-ring. Also we give some examples to show that assumption compatibility on α is not superfluous.

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