J. Płonka in [12] noted that one could expect that the regularization of a variety of unary algebras is a subdirect product of and the variety of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties which are contained in the generalized variety of the so-called trap-directable algebras.
We study groupoids satisfying the identities x·xy = y and x·yz = xy·xz. Particularly, we focus our attention at subdirectlyirreducible ones, find a description and charecterize small ones.
A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables....
The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I. Bethke, P. Rodenburg, and A. Sevenster in their paper (2015), to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as...