부산대학교 도서관

A ring R is called semiclean if every element of R can be expressed as sum of a periodic element and a unit. In this paper, we introduce a new class of ring, which is the *-version of the semiclean ring, i.e. the *-semiclean ring. A *-ring is *-semiclean if each element is a sum of a *-periodic element and a unit. The term *-semiclean is a stronger notion than semiclean. In this paper, many properties of *-semiclean rings are discussed. It is proved that if p ∈ P(R) such that pRp and (1 - p)R(1 - p) are *-semiclean rings, then R is also a *-semiclean ring. As a result, the matrix ring Mn(R) over a *-semiclean ring is *-semiclean. A characterization that when the group rings RCr and RG are *-semiclean is done, where R is a finite commutative local ring, Cr is a cyclic group of order r, and G is a locally finite abelian group. We have also found sufficient conditions when the group rings RC3, RC4, RQ8, and RQ2n are *-semiclean, where R is a commutative local ring. We have also demonstrated that the group ring Z2D6 is a *-semiclean ring (which is not a *-clean ring). [ABSTRACT FROM AUTHOR]