The varieties defined by \(P\)-compatible identities of modular ortholattices
Consider the variety MOL of modular ortholattices with the set \(F:=\{\vee,\wedge,'\}\) of operation symbols and let \(P\) be a partition of \(F\) and \(p=q\) an identity in MOL. The identity \(p=q\) is called \(P\)-compatible if either \(p\) and \(q\) are the same variable or \(p\) and \(q\) are not variables and the outermost operation symbol of \(p\) and that of \(q\) belong to the same block of \(P\). ``Externally compatible'' means \(P\)-compatible where \(P\) consists of singletons only. Let MOL\(_P\) (MOL\(_{Ex}\)) denote the variety defined by the set of all \(P\)-compatible (externally compatible) identities satisfied in MOL. Equational bases of MOL\(_{Ex}\) are explicitly stated, MOL\(_P\) is semantically characterized, and the lattice of some subvarieties of MOL\(_{Ex}\) is described.
scientific article; zbMATH DE number 5822063
scientific article