Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 2107-2117 https://doi.org/10.4134/BKMS.b160774 Published online July 21, 2017 Printed November 30, 2017
Hyun-Min Kim, Dan Li, Zhelin Piao Pusan National University, Pusan National University, Pusan National University
Abstract : We study the quasi-commutativity in relation with powers of coefficients of polynomials. In the procedure we introduce the concept of {\it $\pi$-quasi-commutative} ring as a generalization of quasi-commutative rings. We show first that every $\pi$-quasi-commutative ring is Abelian and that a locally finite Abelian ring is $\pi$-quasi-commutative. The role of these facts are essential to our study in this note. The structures of various sorts of $\pi$-quasi-commutative rings are investigated to answer the questions raised naturally in the process, in relation to the structure of Jacobson and nil radicals.
Keywords : $\pi$-quasi-commutative ring, center, quasi-commutative ring, idempotent, polynomial ring, matrix ring, Abelian ring, locally finite ring
