On monoids presented by a single relation

Lallement, G.

doi:10.1016/0021-8693(74)90146-x

Cited by 43 publications

(51 citation statements)

References 6 publications

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“…In fact, a two-sided semigroup S contains a subset of the form X = {c p+ud b p+vd ; u, v 0}, which is isomorphic to the bicyclic monoid; the mapping ψ : B → X; c u b v → c p+ud b p+vd is clearly an isomorphism. Since B is not residually finite (see [11]) it follows that S is not residually finite either.…”

Section: Residual Finitenessmentioning

confidence: 94%

Properties of the subsemigroups of the bicyclic monoid

Descalço

Ruškuc

2008

Czech Math J

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In this paper we study some properties of the subsemigroups of the bicyclic monoid B, by using a recent description of its subsemigroups. We start by giving necessary and sufficient conditions for a subsemigroup to be finitely generated. Then we show that all finitely generated subsemigroups are automatic and finitely presented. Finally we prove that a subsemigroup of B is residually finite if and only if it does not contain a copy of B.

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Section: Residual Finitenessmentioning

confidence: 94%

Properties of the subsemigroups of the bicyclic monoid

Descalço

Ruškuc

2008

Czech Math J

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“…There are a number of special cases of semigroup presentations with one defining relation for which the word problem is known to be solvable. The publications [13], [21], [6], and [8] are examples. There are other special cases of finite semigroup presentations with solvable word problem which can be applied to presentations with one defining relation.…”

Section: Applications To Semigroups With One Defining Relationmentioning

confidence: 99%

Thickness of Feathers

Cummings

Jackson

2014

Communications in Algebra

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“…Then (A, R) is a confluent noetherian rewriting system and so the monoid M presented by A | R is Markov by Proposition 7.1. This monoid M is known to be non-residually finite [Lal74].…”

Section: Miscellaneous Examples Of Markov and Non-markov Semigroupsmentioning

confidence: 99%

Markov semigroups, monoids and groups

Cain

Maltcev

2014

Int. J. Algebra Comput.

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A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length representatives over every generating set. This paper considers the natural generalizations of these concepts to semigroups and monoids. Two distinct potential generalizations to monoids are shown to be equivalent. Various interesting examples are presented, including an example of a non-Markov monoid that nevertheless admits a regular language of unique representatives over any generating set. It is shown that all finitely generated commutative semigroups are strongly Markov, but that finitely generated subsemigroups of virtually abelian or polycyclic groups need not be. Potential connections with wordhyperbolic semigroups are investigated. A study is made of the interaction of the classes of Markov and strongly Markov semigroups with direct products, free products, and finite-index subsemigroups and extensions. Several questions are posed.

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On monoids presented by a single relation

Cited by 43 publications

References 6 publications

Properties of the subsemigroups of the bicyclic monoid

Properties of the subsemigroups of the bicyclic monoid

Thickness of Feathers

Markov semigroups, monoids and groups

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