On existence of joins and meets under the star order in strong Rickart rings

Abstract

A strong Rickart ring is a Rickart ring which has some special properties that make it similar, in some respects, to Rickart *-rings. It is known that the star partial order on a Rickart *-ring can be characterized by a condition not involving involution; this allows one to define the star order also on strong Rickart rings. In the paper, we reconsider several conditions, known in the literature, for existence of joins and meets in Rickart *-rings under the star order. Our main purpose is to transfer the conditions, even those involving involution, to strong Rickart rings and to show that they are valid also in this wider class of rings.