DIRECT SUMS OF J-RINGS AND RADICAL RINGS

XIUZHAN GUO

《International Journal of Mathematics and Mathematical Sciences》 1995卷 (1995/12) Pp. 531-534

https://doi.org/10.1155/S0161171295000664

摘要

Let R be a ring, J(R) the Jacobson radical of R and P the set of potent elements of R. We prove that if R satisfies(∗) given x, y in R there exist integers m=m(x, y)＞1 and n=n(x, y)＞1 such that x^my=xy^n and if each x ∈ R is the sum of a potent element and a nilpotent element, then N and P are ideals and R=N⊕P. We also prove that if R satisfies (∗) and if each x ∈ R has a representation in the form x= a + u, where a ∈ P and u ∈ J(R), then P is an ideal and R=J(R)⊕P.

關鍵字

Periodic ； potent ； J -ring ； radical ring ； direct sum