相关论文: Rosenberg's classification of maximal clones

Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…

We classify $n$-representation infinite algebras $\Lambda$ of type \~A. This type is defined by requiring that $\Lambda$ has higher preprojective algebra $\Pi_{n+1}(\Lambda) \simeq k[x_1, \ldots, x_{n+1}] \ast G$, where $G \leq…

Clones of functions play a foundational role in both universal algebra and theoretical computer science. In this work, we introduce clone merge monoids (cm-monoids), a unifying one-sorted algebraic framework that integrates abstract clones,…

The starting point of algebraic language theory is that regular languages of finite words are exactly those recognized by finite monoids. This finiteness condition gives rise to a topological space whose points, called profinite words,…

In 1986, the second author classified the minimal clones on a finite universe into five types. We extend this classification to infinite universes and to multiclones. We show that every non-trivial clone contains a "small" clone of one of…

We study the Borel-reducibility of isomorphism relations of complete first order theories and show the consistency of the following: For all such theories T and T', if T is classifiable and T' is not, then the isomorphism of models of T' is…

For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of the other using operations from C. In…

We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…

The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions,…

We describe the ordering of a class of clones by minion homomorphisms, also known as minor preserving maps or height 1 clone homomorphisms. The class consists of all clones on finite sets determined by binary relations whose projections to…

We prove that two finite prime $\Omega$-algebras defined over the same unital commutative ring and satisfying the same set of polynomial identities are isomorphic.

We consider finitary relations (also known as crosses) that are definable via finite disjunctions of unary relations, i.e. subsets, taken from a fixed finite parameter set $\Gamma$. We prove that whenever $\Gamma$ contains at least one…

We investigate an analogue of the Wedderburn principal theorem for associative conformal algebras with finite faithful representations. It is shown that the radical splitting property for an algebra of this kind holds if the maximal…

For representation by partial functions in the signature with intersection, composition and antidomain, we show that a representation is meet complete if and only if it is join complete. We show that a representation is complete if and only…

We investigate when the clone of congruence preserving functions is finitely generated. We obtain a full description for all finite $p$-groups, and for all finite algebras with Mal'cev term and simple congruence lattice. The…

Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…

We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the…

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…

The notion of commutation of operations in universal algebra leads to the concept of centralizer clone and gives rise to a well-known class of problems that we call centralizer problems, in which one seeks to determine whether a given set…

Let 2<n\leq l<m< \omega. Let L_n denote first order logic restricted to the first n variables. We show that the omitting types theorem fails dramatically for the n--variable fragments of first order logic with respect to clique guarded…