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Generalized orthomodular posets. (English) Zbl 0755.06006
The autor generalizes the notion of generalized orthomodular lattices, introduced by Janowitz, to the notion of generalized orthomodular posets GOMP. Every orthomodular poset is a GOMP. Every (weak) GOMP $$A$$ can be embedded as an order ideal in an orthomodular poset $$P$$ such that $$x\in A$$ or $$x^ \bot\in A$$ for every $$x\in P$$. For a GOMP existing suprema $$x\lor y\in A$$ are preserved. Every Rickart *-ring “is” a GOMP.
Reviewer: G.Kalmbach (Ulm)

MSC:
 06C15 Complemented lattices, orthocomplemented lattices and posets