2016•Communications in AlgebraRequires access

Some characterizations of ∗-regular rings

Jian Cui, Xiaobin Yin

Abstract

A ∗-ring R is called ∗-regular if every principal one-sided ideal of R is generated by a projection. The paper is devoted to a study of ∗-regularity of ∗-rings. Basic properties of ∗-regular rings are investigated, and some equivalent characterizations on ∗-regular rings, Abelian ∗-regular rings, and *-unit regular rings are provided. We also show that a matrix ring Mn(R) is ∗-unit regular if and only if R is unit regular and 1+x1∗x1+⋯+xn−1∗xn−1 is a unit for all xi in R.

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Key concepts: Mathematics, Unit (ring theory), Von Neumann regular ring, Principal ideal, Regular ring, Ring (chemistry), Principal ideal ring, Ideal (ethics)