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We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms.

Definability in the lattice of equational theories of semigroups.

J. Jezek, R. McKenzie (1993)

Semigroup forum

Definability of principal congruences in equivalential algebras

PaweŁ Idziak, Andrzej Wroński (1998)

Colloquium Mathematicae

Diamond identities for relative congruences

Gábor Czédli (1995)

Archivum Mathematicum

For a class $K$ of structures and $A \in K$ let ${C o n}^{*} (A)$ resp. ${C o n}^{K} (A)$ denote the lattices of $*$ -congruences resp. $K$ -congruences of $A$ , cf. Weaver [25]. Let ${C o n}^{*} (K) : = I {{C o n}^{*} (A) : A \in K}$ where $I$ is the operator of forming isomorphic copies, and ${C o n}^{r} (K) : = I {{C o n}^{K} (A) : A \in K}$ . For an ordered algebra $A$ the lattice of order congruences of $A$ is denoted by ${C o n}^{<} (A)$ , and let ${C o n}^{<} (K) : = I {{C o n}^{<} (A) : A \in K}$ if $K$ is a class of ordered algebras. The operators of forming subdirect squares and direct products are denoted by $Q^{s}$ and $P$ , respectively. Let $λ$ be a lattice identity and let $Σ$ be a set of lattice identities. Let $Σ ⊧_{c} λ (r; Q^{s}, P)$ denote...

Diassociativity is not finitely based relative to power associativity

Tomasz Kowalski (2010)

Commentationes Mathematicae Universitatis Carolinae

We show that the variety of diassociative loops is not finitely based even relative to power associative loops with inverse property.

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Decidability and structure

Decidability of equational theories of coverings of semigroup varieties.

Decidability of weak equational theories

Decidability problems for the variety generated by tournaments.

Decomposability conditions for compatible relations

Decompositions in lattices and some representations of algebras [Book]

Decompositions of a $C$ -algebra.

Decompositions of homomorphisms

Definability for equational theories of commutative groupoids

Definability in the lattice of equational theories of semigroups.

Definability of principal congruences in equivalential algebras

Diamond identities for relative congruences

Diassociativity is not finitely based relative to power associativity

Different levels of word problems for some varieties.

Direct decomposability of congruences in congruence-permutable varieties

Direct limits of congruence systems

Direct limits of monounary algebras

Direct products of homomorphic mappings. I

Direct products of homomorphic mappings. II

Directly decomposable congruences in varieties with nullary operations

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