A well known theorem of Murskiı̆’s asserts that almost every finite, nonunary algebra is idemprimal. We derive an analagous result under the assumption that all basic operations are idempotent. If the algebra contains a basic l-ary idempotent operation with l > 2 then the algebra is idemprimal with probability 1. However, for an algebra with a single basic binary operation, the probability of id...

First, we introduce the concept of intuitionistic fuzzy group congruenceand we obtain the characterizations of intuitionistic fuzzy group congruenceson an inverse semigroup and a T^{*}-pure semigroup, respectively. Also,we study some properties of intuitionistic fuzzy group congruence. Next, weintroduce the notion of intuitionistic fuzzy semilattice congruence and we givethe characterization of...

Consider a finite group G and subgroups H,K of G. We say that H and K permute if HK = KH and call H a permutable subgroup if H permutes with every subgroup of G. A group G is called quasi-Dedekind if all subgroups of G are permutable. We can define, for every finite group G, an arithmetic quantity that measures the probability that two subgroups (chosen uniformly at random with replacement) per...

In this paper we investigate the computational complexity of deciding if a given finite algebraic structure satisfies a certain type of existential condition on its set of term operations. These conditions, known as Maltsev conditions, have played a central role in the classification, study, and applications of general algebraic structures. Several well studied properties of equationally define...

The theory of linear lattices is presented as a system with multiple-conclusion rules. It is shown through the permutability of the rules that the system enjoys a subterm property: all terms in a derivation can be restricted to terms in the conclusion or in the assumptions. Decidability of derivability with the rules for linear lattices follows through the termination of proof-search.

The conformal geometry of spacelike surfaces in 4-dimensional Lorentzian space forms has been studied by the authors in a previous paper, where the so-called polar transform was introduced. Here it is shown that this transform preserves spacelike conformal isothermic surfaces. We relate this new transform with the known transforms (Darboux transform and spectral transform) of isothermic surface...