We characterize the finite-dimensional elements of a free cylindric algebra. This solves Problem 2.10 in [Henkin, Monk, Tarski: Cylindric Algebras, North-Holland, 1971 and 1985]. We generalize the characterization to quasivarieties of Boolean algebras with operators in place of cylindric algebras. Free algebras play an important role in universal algebra, see e.g. AndrékaJónsson-Németi [2]. Fre...

We expand the notion of characteristic formula to infinite finitely presentable subdirectly irreducible algebras. We prove that there is a continuum of varieties of Heyting algebras containing infinite finitely presentable subdirectly irreducible algebras. Moreover, we prove that there is a continuum of intermediate logics that can be axiomatized by characteristic formulas of infinite algebras ...

In this study, we examine multiple algebras and algebraic structures derived from them and by stating a theory on multiple algebras; we will show that the theory of multiple algebras is a natural extension of the theory of universal algebras. Also, we will treat equivalence relations on multiple algebras, for which the quotient constructed modulo them is a universal algebra and will study the b...

In this paper we discuss some recent results on two diierent types of growth of Lie algebras, that lead to some combinatorial problems. First, we study the growth of nitely generated Lie algebras (sections 1{4). This problem leads to a study of generalized partitions. Recently the author has suggested a series of q-dimensions of algebras Dim q , q 2 N which includes, as rst terms, dimensions of...

The paper investigates idempotent, reductive, and distributive groupoids, and more generally Ω-algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left k-step reductive Ω-algebras, and of right n-step reductive Ω-algebras, are indep...

The main contribution of this paper is the construction of a strong duality for the varieties generated by a set of subalgebras of a semi-primal algebra. We also obtain an axiomatization of the objects of the dual category and develop some algebraic consequences (description of the dual of the finite structures and algebras, construction of finitely generated free algebras,. . . ). Eventually, ...

We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by socalled adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the sam...