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A reduced Rickart ring is considered as a reduced ring R with an additional operation which associates to every element $$a \in R$$ a∈R the single idempotent e such that the ideal eR is the right annihilator of a. We discuss some elementary properties of this operation, prove that a ring is reduced and Rickart if and only if it is isomorphic to an associate ring in the sense of I. Sussman (a certain...
A nearlattice A is a meet semilattice in which every initial segment is a lattice; A is said to be Boolean if all of these lattices are Boolean. Overriding on A is a binary operation defined by $ a \triangleleft {b} := \sup\{x\colon (x \le a \mbox{ and } x {\mathrel{\mbox{\,\raisebox{.7ex}{$\scriptstyle|$}\hspace{-.75ex}\raisebox{-.35ex}{$\circ$}}}}b) \mbox{ or } x \le b\} $...
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