Finiteness properties of direct products of algebraic structures

@article{Mayr2016FinitenessPO,
  title={Finiteness properties of direct products of algebraic structures},
  author={Peter Mayr and Nik Ru{\vs}kuc},
  journal={arXiv: Rings and Algebras},
  year={2016}
}

Generating subdirect products

TLDR
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.

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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

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presented lattices and their finitely generated sublattices satisfying Dean’s condition (D), which generalizes an unpublished result of Freese and Nation.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

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