Varieties of Birkhoff systems. I
A Birkhoff system is an algebra with two binary operations \(+\) and \(\cdot\) which are commutative, associative, idempotent and satisfy the identity \(x\cdot(x+y)=x+(x\cdot y)\). Examples of Birkhoff systems are lattices, quasilattices and the regularization of the variety of lattices. The authors study the lattice of subvarieties of Birkhoff systems. In particular, they investigate splitting varieties, varieties which form a bottom of the lattice of varieties of Birkhoff systems, quasilattices, distributive bisemilattices, varieties generated by bichains, splitting pairs and varieties generated by three element bichains.
scientific article; zbMATH DE number 6706483
scientific article