Subdirect Products of Rings without *-Reversible Elements

Wafaa Mohammed Fakieh

Department of Mathematics, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia.

Abstract: A left (right) zero divisor a ∈ R is called right (left) *-reversible if ax = 0(xa = 0), for x ∈ R, x ≠ 0, then xa* = 0(a*x = 0). In this note we prove that a *-prime involution ring is a *-compressible if and only if it has no *-reversible element. Moreover, we show that semiprime ring with involution R is a subdirect product of ring without *-reversible elements if and only if R is *-compressible. Several results related to *-compressible ring are obtained.

Keywords: *-reversible element, *-compressible ring.

Pages: 296 – 301 | Full PDF Paper