Algebraic Aspects of Orthomodular Lattices

In this survey article we try to give an up-to-date account of certain aspects of the theory of ortholattices (abbreviated OLs), orthomodular lattices (abbreviated OMLs) and modular ortholattices (abbreviated MOLs), not hiding our own research interests. Since most of the questions we deal with have their origin in Universal Algebra, we start with a section discussing the basic concepts and results of Universal Algebra without proofs. In the next three sections we discuss, mostly with proofs, the basic results and standard techniques of the theory of OMLs. In the remaining five sections we work our way to the border of present day research, with no or only sketchy proofs. Section 5 deals with products and subdirect products, section 6 with free structures and section 7 with classes of OLs defined by equations. In section 8 we discuss embeddings of OLs into complete ones. The last section deals with questions originating in Category Theory, mainly amalgamation, epimorphisms and monomorphisms. The later sections of this paper contain an abundance of open problems. We hope that this will initiate further research.