[HTML][HTML] Semi-abelian categories

G Janelidze, L Márki, W Tholen - Journal of Pure and Applied Algebra, 2002 - Elsevier
The notion of semi-abelian category as proposed in this paper is designed to capture typical
algebraic properties valid for groups, rings and algebras, say, just as abelian categories …

[图书][B] The shape of congruence lattices

K Kearnes, E Kiss - 2013 - ams.org
We develop the theories of the strong commutator, the rectangular commutator, the strong
rectangular commutator, as well as a solvability theory for the nonmodular TC commutator …

[图书][B] Lattice theory: special topics and applications

GA Gratzer, F Wehrung - 2016 - Springer
George Grätzer started writing his General Lattice Theory in 1968. It was published in 1978.
It set out “to discuss in depth the basics of general lattice theory.” Almost 900 exercises, 193 …

On the complexity of some Maltsev conditions

R Freese, MA Valeriote - International Journal of Algebra and …, 2009 - World Scientific
This paper studies the complexity of determining if a finite algebra generates a variety that
satisfies various Maltsev conditions, such as congruence distributivity or modularity. For …

Notes on csps and polymorphisms

Z Brady - arXiv preprint arXiv:2210.07383, 2022 - arxiv.org
These are notes from a multi-year learning seminar on the algebraic approach to Constraint
Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structures …

A solution to Dilworth's congruence lattice problem

F Wehrung - Advances in Mathematics, 2007 - Elsevier
We construct an algebraic distributive lattice D that is not isomorphic to the congruence
lattice of any lattice. This solves a long-standing open problem, traditionally attributed to RP …

Correspondences between Gentzen and Hilbert systems

JG Raftery - The Journal of Symbolic Logic, 2006 - cambridge.org
Most Gentzen systems arising in logic contain few axiom schemata and many rule
schemata. Hilbert systems, on the other hand, usually contain few proper inference rules …

A finite basis theorem for residually finite, congruence meet-semidistributive varieties

R Willard - The Journal of Symbolic Logic, 2000 - cambridge.org
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 …

Assertionally equivalent quasivarieties

WJ Blok, JG Raftery - International Journal of Algebra and …, 2008 - World Scientific
A translation in an algebraic signature is a finite conjunction of equations in one variable. On
a quasivariety K, a translation τ naturally induces a deductive system, called the τ …

The lattice of lambda theories

S Lusin, A Salibra - Journal of Logic and Computation, 2004 - ieeexplore.ieee.org
Lambda theories are equational extensions of the untyped lambda calculus that are closed
under derivation. The set of lambda theories is naturally equipped with a structure of …