Retract irreducibility of monounary algebras
Retract varieties of lattice ordered groups
Retract varieties of monounary algebras
Retracts and Q-independence
A non-empty set X of a carrier A of an algebra A is called Q-independent if the equality of two term functions f and g of the algebra A on any finite system of elements a₁,a₂,...,aₙ of X implies f(p(a₁),p(a₂),...,p(aₙ)) = g(p(a₁),p(a₂),...,p(aₙ)) for any mapping p ∈ Q. An algebra B is a retract of A if B is the image of a retraction (i.e. of an idempotent endomorphism of B). We investigate Q-independent subsets of algebras which have a retraction in their set of term functions.
Ring varieties closed under ideal sums
Selfdistributive groupoids. Part D1: Left distributive semigroups
Selfdistributive grupoids, Part A2: Non-idempotent left distributive quasigroups
Semidirectly closed pseudovarieties of locally trivial semigroups.
Semigroups with idempotent powers, II: The lattices of equational subclasses of [(xy2 =xy] .
Semiregularity of congruences implies congruence modularity at 0
We introduce a weakened form of regularity, the so called semiregularity, and we show that if every diagonal subalgebra of is semiregular then is congruence modular at 0.
Sets with two associative operations
In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.
Sheaf Spaces and Sheaves of Universal Algebras.
Shift-automorphism methods for inherently nonfinitely based varieties of algebras
Simple and subdirectly irreducibles bounded distributive lattices with unary operators.
Slim groupoids
Slim groupoids are groupoids satisfying . We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such groupoids are inherently nonfinitely based) and find all strongly nonfinitely based slim groupoids with at most four...
Small idempotent clones. I
G. Grätzer and A. Kisielewicz devoted one section of their survey paper concerning -sequences and free spectra of algebras to the topic “Small idempotent clones” (see Section 6 of [18]). Many authors, e.g., [8], [14, 15], [22], [25] and [29, 30] were interested in -sequences of idempotent algebras with small rates of growth. In this paper we continue this topic and characterize all idempotent groupoids with (see Section 7). Such groupoids appear in many papers see, e.g. [1], [4], [21], [26,...
Solid varieties of semigroups.
Solvability of equations in varieties of universal algebras.
Some algebraic properties of weakly compact and compact cardinals
Some decidable theories with finitely many covers which are decidable and algorithmically found
In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely based decidable...