圈乘正则子环的和

Sum of Adjoint Regular Subrings

研究环圈乘半群的正则性.给出了圈乘正则环的一个刻画,当环R是两个圈乘正则子环之和时,给出了R的圈乘半群是正则半群的条件,推广了Volkov等人的相关结果,并证实了他们的一个猜测.

This note deals with the regularity of the adjoint semigroup of a ring. A characterization of adjoint regular rings is presented. For ring R which is a sum of two adjoint regular subrings, sufficient and necessary conditions for the regularity of the adjoint semigroup of R are given, which have extend the results given by Volkov and Tanana, and affirm their conjecture.