Abstract:

Considering the quasiArmendariz property of the subring S_n(R) of n×n matrix ring M_n(R), the author proved that if R is a semiprime ring with compatible endomorphisms α₁,α₂,…,α_n, then S_n(R) is a quasiArmendariz ring for any positive integer n≥2, and that if R is a commutative ring and α₁,α₂,…,α_n are compatible endomorphisms of R such that α₁=α_n, then R is a semiprime ring if and only if Sn(R) is a quasiArmendariz ring.

Key words: quasi-Armendariz ring, semiprime ring, compatible endomorphism