Research output: Research - peer-review › Article

We consider the preservation of properties of being finitely generated, being finitely presented and being residually finite under direct products in the context of different types of algebraic structures. The structures considered include Mal’cev algebras (including groups, rings and other classical algebras, as well as loops), idempotent algebras (including lattices), semigroups, and algebras in congruence modular varieties. We aim to identify as broadclasses as possible in which the ‘expected’ preservation results (**A** × **B** satisfies property P if and only if **A** and **B** satisfy P) hold, and to exhibit ways in which they may fail outside those classes.

Original language | English |
---|---|

Pages (from-to) | 167-187 |

Journal | Journal of Algebra |

Volume | 494 |

Early online date | 3 Nov 2017 |

DOIs | |

State | Published - 15 Jan 2018 |

Additional links |

- Finitely generated, Finitely presented, Residual finite

**Discover related content**

Find related publications, people, projects and more using interactive charts.

## Finite presentability and isomorphism of Cayley graphs of monoids

Awang, J. S., Pfeiffer, M. J. & Ruskuc, N. Nov 2017 In : Proceedings of the American Mathematical Society. 145, 11, p. 4585-4593Research output: Research - peer-review › Article

## On well quasi-order of graph classes under homomorphic image orderings

Huczynska, S. & Ruškuc, N. Jun 2017 In : European Journal of Combinatorics. 63, p. 164-175 12 p.Research output: Research - peer-review › Article

## On regularity and the word problem for free idempotent generated semigroups

Dolinka, I., Gray, R. D. & Ruskuc, N. 3 Mar 2017 In : Proceedings of the London Mathematical Society. 114, 3, p. 401-432 32 p.Research output: Research - peer-review › Article

## Free monoids are coherent

Gould, V., Hartmann, M. & Ruskuc, N. Feb 2017 In : Proceedings of the Edinburgh Mathematical Society. 60, 1, p. 127-131 5 p.Research output: Research - peer-review › Article

## On the star-height of subword counting languages and their relationship to Rees zero-matrix semigroups

Bourne, T. & Ruškuc, N. 15 Nov 2016 In : Theoretical Computer Science. 653, p. 87-96Research output: Research - peer-review › Article

## Minimal and canonical images

Jefferson, C., Jonauskyte, E., Pfeiffer, M. & Waldecker, R. 3 Apr 2018 (Accepted/In press) In : Journal of Algebra.Research output: Research - peer-review › Article

## Maximal subsemigroups of finite transformation and diagram monoids

East, J., Kumar, J., Mitchell, J. D. & Wilson, W. A. 21 Feb 2018 In : Journal of Algebra. 504, p. 176-216Research output: Research - peer-review › Article

## Imprimitive permutations in primitive groups

Araújo, J., Araújo, J. P., Cameron, P. J., Dobson, T., Hulpke, A. & Lopes, P. 15 Sep 2017 In : Journal of Algebra. 486, p. 396-416Research output: Research - peer-review › Article

## Decision problems for word-hyperbolic semigroups

Cain, A. J. & Pfeiffer, M. J. 1 Nov 2016 In : Journal of Algebra. 465, p. 287-321Research output: Research - peer-review › Article

ID: 251454222