ON SEMI-ARMENDARIZ MATRIX RINGS

Title & Authors
ON SEMI-ARMENDARIZ MATRIX RINGS
KOZLOWSKI, KAMIL; MAZUREK, RYSZARD;

Abstract
Given a positive integer n, a ring R is said to be n-semi-Armendariz if whenever $\small{f^n=0}$ for a polynomial f in one indeterminate over R, then the product (possibly with repetitions) of any n coefficients of f 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.
Keywords
n-semi-Armendariz ring;semi-Armendariz ring;upper triangular matrix ring;
Language
English
Cited by
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