Related papers: Characterizing the commutator in varieties with a …

We show that the modular term condition higher commutator is equal to the modular hypercommutator. As a consequence, we arrive at a new proof that HC8 holds for modular varieties. Next, we develop a procedure for a modular variety for…

We develop the basic properties of the higher commutator for congruence modular varieties.

We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.

We consider the following practical question: given a finite algebra A in a finite language, can we efficiently decide whether the variety generated by A has a difference term? We answer this question (positively) in the idempotent case and…

We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.

A distinguished variety is a variety that exits the bidisk through the distinguished boundary. We show that Ando's inequality for commuting matrix contractions can be sharpened to looking at the maximum modulus on a distinguished variety,…

We provide a partial result on Taylor's modularity conjecture, and several related problems. Namely, we show that the interpretability join of two idempotent varieties that are not congruence modular is not congruence modular either, and we…

We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then…

We study the transfer of (co)silting objects in derived categories of module categories via the extension functors induced by a morphism of commutative rings. It is proved that the extension functors preserve (co)silting objects of…

We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…

We prove the definability, and actually the finiteness of the commutator width, of many commutator subgroups in groups definable in o-minimal structures. It applies in particular to derived series and to lower central series of solvable…

We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples…

Finding functions, particularly permutations, with good differential properties has received a lot of attention due to their varied applications. For instance, in combinatorial design theory, a correspondence of perfect $c$-nonlinear…

In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…

In this paper we recall the construction and basic properties of complex Shimura varieties and show that these properties actually characterize them. This characterization immediately implies the explicit form of Kazhdan's theorem on the…

Congruence modular and congruence distributive varieties can be characterized by the existence of sequences of Gumm and J\'onsson terms, respectively. Such sequences have variable lengths, in general. It is immediate from the above…

We study the coherence and conservativity of extensions of dependent type theories by additional strict equalities. By considering notions of congruences and quotients of models of type theory, we reconstruct Hofmann's proof of the…

Motivated by the theory of domination for types, we introduce a notion of domination for Keisler measures called extension domination. We argue that this variant of domination behaves similarly to its type setting counterpart. We prove that…

We investigate from an algebraic and topological point of view the minimal prime spectrum of a universal algebra, considering the prime congruences w.r.t. the term condition commutator. Then we use the topological structure of the minimal…

We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between…