For n a positive integer and K a finite set of finite algebras, let L(n,K) denote the largest n-generated subdirect product whose subdirect factors are algebras in K. When K is the set of all ngenerated subdirectly irreducible algebras in a locally finite variety V, then L(n,K) is the free algebra FV(n) on n free generators for V. For a finite algebra A the algebra L(n, {A}) is the largest n-ge...

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...

‎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.

In other words, SA is the variety of semilattices with one automorphism (which is, as well as its inverse, considered as an additional fundamental operation). The aim of this paper is to find all subdirectly irreducible algebras in SA . A universal algebra A is said to be subdirectly irreducible (shortly, an SI algebra) if it contains more than one element and among all the nontrivial congruenc...