# Finite Complete Rewriting Systems and Finite Derivation Type for Small Extensions of Monoids

@article{Wang1998FiniteCR, title={Finite Complete Rewriting Systems and Finite Derivation Type for Small Extensions of Monoids}, author={J. Wang}, journal={Journal of Algebra}, year={1998}, volume={204}, pages={493-503} }

Abstract LetSbe a monoid and letTbe a submonoid of finite index inS. The main results in this article state thatScan be presented by a finite complete rewriting system ifTcan, andShas finite derivation type ifThas.

## 26 Citations

Finite Derivation Type Property on the Chinese Monoid

- Mathematics
- 2010

Squier introduced the notion finite derivation type which is a combinatorial condition satisfied by certain rewriting systems. The main result in this paper states that the Chinese monoid has finite…

Finite Derivation Type for Graph Products of Monoids

- Mathematics
- 2016

The aim of this paper is to show that the class of monoids of finite derivation type is closed under graph products.

Finite Derivation Type for Semigroups and Congruences

- Mathematics
- 2007

We consider a congruence ρ on a semigroup S as a subsemigroup of the direct product S × S. We prove that if ρ has finite derivation type (FDT), then so does S.

On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids

- MathematicsInf. Comput.
- 2017

IDEALS AND FINITENESS CONDITIONS FOR SUBSEMIGROUPS

- MathematicsGlasgow Mathematical Journal
- 2013

Abstract In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroups with…

Finite derivation type for large ideals

- Mathematics
- 2008

In this paper we give a partial answer to the following question: does a large subsemigroup of a semigroup S with the finite combinatorial property finite derivation type (FDT) also have the same…

Automatic Semigroups with Subsemigroups of Finite Rees Index

- MathematicsInt. J. Algebra Comput.
- 2002

The notion of automaticity has been widely studied in groups and some progress has been made in understanding this notion in the wider context of semigroups. The purpose of this paper is to study t...

Presentations for Subgroups of Monoids

- Mathematics
- 1999

Abstract The main result of this paper gives a presentation for an arbitrary subgroup of a monoid defined by a presentation. It is a modification of the well known Reidemeister–Schreier theorem for…

## References

SHOWING 1-10 OF 14 REFERENCES

Finite Derivation Type Implies the Homological Finiteness Condition FP_3

- MathematicsJ. Symb. Comput.
- 1994

A partial result is established by showing that for finitely presented monoids the property of having finite derivation type implies the homological finiteness conditions FP3, and that the property FP3 is strictly weaker than the property.

On Large Subsemigroups and Finiteness Conditions of Semigroups

- Mathematics
- 1998

Let be a semigroup and let be a subsemigroup of . We say that is if the set is finite. Alternatively, we say that is a of . The cardinality of the set is called the of in , and is denoted by [ : ].…

On Subsemigroups and ideals in Free Products of Semigroups

- MathematicsInt. J. Algebra Comput.
- 1996

It is proved that the free product of any two semigroups, at least one of which is nontrivial, contains a two-sided ideal which is not finitely generated as a semigroup, and also contains a subsemigroup which is finitely generate but not finally presented.

Semigroups, Formal Languages and Groups

- Mathematics
- 1899

Foreword. Finite semigroups and Recognizable Languages J. E. Pin. BG=PG: A Success Story J. E. Pin. Semigroups and Automata on Infinite Words D. Perrin, J. E. Pin. Relatively Free Profinite Monoids…

On Subsemigroups of Finitely Presented Semigroups

- Mathematics
- 1996

The purpose of this paper is to investigate properties of subsemigroups of finitely presented semigroups, particularly with respect to the property of being finitely presented. More precisely, we…