Finiteness properties of direct products of algebraic structures

  title={Finiteness properties of direct products of algebraic structures},
  author={Peter Mayr and Nik Ru{\vs}kuc},
  journal={arXiv: Rings and Algebras},

Generating subdirect products

Conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented are studied, and general results for arbitrary congruence permutable varieties are proved.

Presentations for P^K

It is a classical result that the direct product A×B of two groups is finitely generated (finitely presented) if and only if A and B are both finitely generated (finitely presented). This is also

Generators and presentations for direct and wreath products of monoid acts

We investigate the preservation of the properties of being finitely generated and finitely presented under both direct and wreath products of monoid acts. A monoid M is said to preserve property

Residual finiteness and related properties in monounary algebras and their direct products

In this paper we discuss the relationship between direct products of monounary algebras and their components, with respect to the properties of residual finiteness, strong/weak subalgebra

Bounded homomorphisms and finitely generated fiber products of lattices

An (exponential time) algorithm is obtained to decide boundedness for finitely presented lattices and their finitely generated sublattices satisfying Dean’s condition (D), which generalizes an unpublished result of Freese and Nation.

Presentations for wreath products involving symmetric inverse monoids and categories

Wreath products involving symmetric inverse monoids/semigroups/categories arise in many areas of algebra and science, and presentations by generators and relations are crucial tools in such studies.



On residual finiteness of direct products of algebraic systems

It is well known that if two algebraic structures A and B are residually finite then so is their direct product. Here we discuss the converse of this statement. It is of course true if A and B

Generators and relations of direct products of semigroups

The purpose of this paper is to give necessary and sufficient; conditions for the direct product of two semigroups to be finitely generated, and also for the direct product to be finitely presented.

On Finite Presentability of Direct Products of Semigroups

A finite semigroup S is said to preserve finite generation (resp., presentability) in direct products, provided that, for every infinite semigroup T, the direct product S × T is finitely generated

Structure and finiteness properties of subdirect products of groups

We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN

On the Structure of Finitely Presented Lattices

A lattice L is finitely presented (or presentable) if and only if it can be described with finitely many generators and finitely many relations. Equivalently, L is the lattice freely generated by a

On multiplicative systems defined by generators and relations

  • T. Evans
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1953
The techniques developed in (9) are used here to study the properties of multiplicative systems generated by one element (monogenie systems). The results are of two kinds. First, we obtain fairly

On the finite presentation of subdirect products and the nature of residually free groups

We establish {\it virtual surjection to pairs} (VSP) as a general criterion for the finite presentability of subdirect products of groups: if $\Gamma_1,\ldots,\Gamma_n$ are finitely presented and

Sublattices of a Free Lattice

  • B. Jónsson
  • Mathematics
    Canadian Journal of Mathematics
  • 1961
Professor R. A. Dean has proved (1, Theorem 3) that a completely free lattice generated by a countable partially ordered set is isomorphic to a sublattice of a free lattice. In particular, it follows

Combinatorial Group Theory

Chapter I. Free Groups and Their Subgroups 1. Introduction 2. Nielsen's Method 3. Subgroups of Free Groups 4. Automorphisms of Free Groups 5. Stabilizers in Aut(F) 6. Equations over Groups 7.