Any mapping S : C → K, where K is a field and C = (C,Σ) is a Σ-algebra, is called a KC-series. These series are natural generalizations of both formal series on strings over a field and the tree series introduced by Berstel and Reutenauer [1]. We consider various operations on KC-series and their effects on the linear extensions of the series. We also study some algebraic aspects of theKΣ-algeb...

We prove that the semirings of 1-preserving and of 0,1preserving endomorphisms of a semilattice are always subdirectly irreducible and we investigate under which conditions they are simple. Subsemirings are also investigated in a similar way.

Although it is well known that the variety of all lattices is generated by the subclass of finite lattices, there are lattice varieties which are not generated by their finite members . In fact, there are modular varieties which are not even generated by their finite dimensional members [3]. At the present t ime it is not known if the variety of all modular lattices is generated by its finite o...

Axiomatizability, the finite model property (FMP), and decidability are some of the most frequently studied properties of non-classical logics. One of the first general methods of axiomatizing large classes of superintuitionistic logics (si-logics for short) was developed by Jankov [8]. For each finite subdirectly irreducible Heyting algebra A, Jankov designed a formula that encodes the structu...

‎In this paper‎, ‎we characterize and find the number of subdirectly‎ ‎irreducible acts over some classes of semigroups‎, ‎such as zero‎ ‎semigroups‎, ‎right zero semigroups‎ ‎and strong chain of left zero semigroups.

In this paper some properties of epi-representations and Schmidt-congruence relations of orthomodular partial algebras are investigated and an infinite list of OMA-episubdirectly irreducible orthomodular partial algebras will be constructed.

This is an expository account of R. McKenzie’s recent refutation of the RS conjecture. We adopt the usual conventions: if S is an algebra then S denotes the universe of S, |S| denotes the cardinality of S, and |S| denotes the successor cardinal to |S|. For an algebra A, let Vsi(A) denote the class of all nontrivial subdirectly irreducible members of V(A), and (following McKenzie) define κ(A) = ...

This is the second part of a two-part paper on Birkhoff systems. A Birkhoff system is an algebra that has two binary operations · and +, with each being commutative, associative, and idempotent, and together satisfying x · (x + y) = x + (x · y). The first part of this paper described the lattice of subvarieties of Birkhoff systems. This second part continues the investigation of subvarieties of...