ON STAR, SHARP, CORE, AND MINUS PARTIAL ORDERS IN RICKART RINGS

Let A be a Rickart *-ring and let <=*, <=(#), <=(circle plus) and <=(circle plus) denote the star, the sharp, the core, and the dual core partial orders in A, respectively. The sets of all b is an element of A such that a <= b, along with the sets of all b is an element of A such that b <= a, are characterized, where a is an element of A is given and where <= is one of the partial orders: <*, or <=(#) or <=(circle plus), or <=(circle plus). Such sets of elements that are above or below a given element under the minus partial order <=(-) in a Rickart ring A are also studied. Some recent results of Cvetkovie-Ilie et al. on partial orders in B(H), the algebra of all bounded linear operators on a Hilbert space H, are thus generalized.