ON SEMI-ARMENDARIZ MATRIX RINGS
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Given a positive integer n, a ring R is said to be n-semi- Armendariz if whenever ∫n = 0 for a polynomial ∫ in one indeterminate over R, then the product (possibly with repetitions) of any n coefficients of ∫ is equal to zero. A ring R is said to be semi-Armendariz if R is n-semi-Armendariz for every positive integer n. Semi-Armendariz rings are a generalization of Armendariz rings. We characterize when certain important matrix rings are n-semi-Armendariz, generalizing some results of Jeon, Lee and Ryu from their paper (J. Korean Math. Soc. 47 (2010), 719–733), and we answer a problem left open in that paper.
Abstract
Given a positive integer n, a ring R is said to be n-semi- Armendariz if whenever ∫n = 0 for a polynomial ∫ in one indeterminate over R, then the product (possibly with repetitions) of any n coefficients of ∫ is equal to zero. A ring R is said to be semi-Armendariz if R is n-semi-Armendariz for every positive integer n. Semi-Armendariz rings are a generalization of Armendariz rings. We characterize when certain important matrix rings are n-semi-Armendariz, generalizing some results of Jeon, Lee and Ryu from their paper (J. Korean Math. Soc. 47 (2010), 719–733), and we answer a problem left open in that paper.
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