Bases for equational theories of semigroups

Perkins, P. G.

doi:10.1016/0021-8693(69)90058-1

Cited by 245 publications

(156 citation statements)

References 4 publications

Supporting

Mentioning

153

Contrasting

Order By: Relevance

“…The proposition above improves Theorem 16 in [27], where the same was proved for n = 2qk + 1. Moreover, our bound is the best possible, as the following example shows.…”

Section: Finite Semigroupssupporting

confidence: 71%

“…In the last section, we apply our results to finite semigroups. In particular, we improve Perkins' result [27] on the number of variables in an equational base of a finitely generated commutative semigroup, and characterize those varieties in ¿'(Com), which are generated by a finite semigroup. The latter turn out to form a sublattice of ¿'(Com).…”

Section: Introductionmentioning

confidence: 94%

“…In a positive direction, Perkins [27] showed that every equational theory of commutative semigroups is finitely based, and hence J? (Com) is countable and has no infinite descending chains.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Varieties of Commutative Semigroups

Kisielewicz¹

1994

Transactions of the American Mathematical Society

View full text Add to dashboard Cite

Abstract.In this paper, we describe all equational theories of commutative semigroups in terms of certain well-quasi-orderings on the set of finite sequences of nonnegative integers. This description yields many old and new results on varieties of commutative semigroups. In particular, we obtain also a description of the lattice of varieties of commutative semigroups, and we give an explicit uniform solution to the word problems for free objects in all varieties of commutative semigroups.

show abstract

“…The proposition above improves Theorem 16 in [27], where the same was proved for n = 2qk + 1. Moreover, our bound is the best possible, as the following example shows.…”

Section: Finite Semigroupssupporting

confidence: 71%

Section: Introductionmentioning

confidence: 94%

See 1 more Smart Citation

Varieties of Commutative Semigroups

Kisielewicz¹

1994

Transactions of the American Mathematical Society

View full text Add to dashboard Cite

show abstract

“…In this section we will give an elementary proof that B 1 2 is not finitely related. The Brandt monoid arises repeatedly in investigations: Perkins proved that it is not finitely based in [26]. Seif [33] and Klíma [22] showed that checking term equivalence for B 1 2 is coNP-complete.…”

Section: A Non-finitely Related Semigroupmentioning

confidence: 99%

On finitely related semigroups

Mayr

2012

Semigroup Forum

View full text Add to dashboard Cite

An algebraic structure is finitely related (has finite degree) if its term functions are determined by some finite set of finitary relations. We show that the following finite semigroups are finitely related: commutative semigroups, 3-nilpotent monoids, regular bands, semigroups with a single idempotent, and Clifford semigroups. Further we provide the first example of a semigroup that is not finitely related: the 6-element Brandt monoid.

show abstract

“…Let us recall that by virtue of [12] every equational theory of commutative semigroups is finitely generated. This means that considering definability of individual theories we may concentrate on one-based theories.…”

Section: Equations and Groups Of Permutationsmentioning

confidence: 99%