# ON SEMI-ARMENDARIZ MATRIX RINGS

• KOZLOWSKI, KAMIL (Faculty of Computer Science Bialystok University of Technology) ;
• MAZUREK, RYSZARD (Faculty of Computer Science Bialystok University of Technology)
• Published : 2015.06.01

#### Abstract

Given a positive integer n, a ring R is said to be n-semi-Armendariz if whenever $f^n=0$ 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.

#### Acknowledgement

Supported by : University of Warsaw

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