## 7 Citations

### Generating subdirect products

- MathematicsJ. Lond. Math. Soc.
- 2019

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

- Mathematics
- 2021

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

- MathematicsSemigroup Forum
- 2018

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

- Mathematics
- 2020

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

- MathematicsInt. J. Algebra Comput.
- 2020

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presented lattices and their finitely generated sublattices satisfying Dean’s condition (D), which generalizes an unpublished result of Freese and Nation.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

- Mathematics
- 2022

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.…

## References

SHOWING 1-10 OF 19 REFERENCES

### On residual finiteness of direct products of algebraic systems

- Mathematics
- 2009

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

- Mathematics
- 1998

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

- Mathematics
- 2000

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

- Mathematics
- 2009

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

- MathematicsCanadian Journal of Mathematics
- 1981

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

- MathematicsMathematical 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

- Mathematics
- 2012

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

- MathematicsCanadian 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

- Mathematics
- 1977

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.…