LEFT T-IDEMPOTENCE AND LEFT T-STABILITY OF SEMIGROUP RINGS

Abstract

A ring R is called left T-idempotent (left T-stable) if for any sequence r ₁,r ₂,… in R there exists a positive integer n such that r ₁ r ₂… r_n is an idempotent (r ₁ r ₂… r_n = r ₁ r ₂… r _n+1 = …). In this paper we characterize left T-idempotent rings and left T-stable rings and describe left T-idempotent semigroup rings and left T-stable semigroup rings.

ACKNOWLEDGMENT

This work was carried out while the author was visiting Symbol Computation and Knowledge Engineering Open Laboratory of Education Ministry of State. The author wishes to thank the members of the laboratory for their hospitality. The author also expresses his gratitude to the referee for helpful comments. This work is supported by Visiting Scholar Foundation of Key Lab, in University.