Related papers: Finitely Based Congruence Varieties

We establish a direct correspondence between two congruence poroperties for finite algebras. The first property is that minimal sets of type i omit tails. The second property is that congruence lattices omit pentagons of type i.

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

We construct a finitely generated group that does not satisfy the generalized Burghelea conjecture.

A variety of universal algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. Until recently, only two explicit examples of limit varieties of monoids, constructed by Jackson, were known.…

While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…

For every $n \in \mathbb{N}$, we construct a variety of Heyting algebras, whose $n$-generated free algebra is finite but whose $(n+1)$-generated free algebra is infinite.

In this paper we prove that in classifying of complex filiform Leibniz algebras, for which its naturally graded algebra is non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we establish a criterion…

We prove a super-rigidity result for algebraic representations over complete fields of irreducible lattices in product of groups and lattices with dense commensurator groups. We derive some criteria for non-linearity of such groups.

For finitary regular monads T on locally finitely presentable categories we characterize the finitely presentable objects in the category of T-algebras in the style known from general algebra: they are precisely the algebras presentable by…

This contains Part I of the book: Congruence lattices of finite lattices, which covers about 80 years of research and more than 250 papers.

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…

We consider the closure space on the set of strings of a gentle algebra of finite representation type. Palu, Pilaud, and Plamondon proved that the collection of all biclosed sets of strings forms a lattice, and moreover, that this lattice…

We review recent results on congruence lattices of (infinite) lattices. We discuss results obtained with box products, as well as categorical, ring-theoretical, and topological results.

We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite composition series whose factors are either reductive or proper, flat, finitely presented, acting on algebraic stacks with affine,…

In this paper we introduce and study a variety of algebras that properly includes integral distributive commutative residuated lattices and weak Heyting algebras. Our main goal is to give a characterization of the principal congruences in…

We give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singularities of closure of conjugacy classes in classical Lie…

We construct non-isogenous simple ordinary abelian varieties over an algebraic closure of a finite field with isomorphic endomorphism algebras.

The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various…

Varieties of quantitative algebras are fully described by their free-algebra monads on the category Met of metric spaces. For a longer time it has been an open problem whether the resulting enriched monads are precisely the strongly…

We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.