Finite semigroups with few term operations

Crvenković, Siniša; Dolinka, Igor; Ruškuc, Nik

doi:10.1016/s0022-4049(00)00017-7

Cited by 11 publications

(10 citation statements)

References 12 publications

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“…We end the paper with some examples which were encountered in our previous investigations [5] and [8]. In the final, third example, we elaborate a bit further the second case of the above theorem.…”

Section: The Main Resultsmentioning

confidence: 76%

“…EXAMPLE 3.6. By Theorem 5.3 of [5], finite semigroups with a p n -sequence bounded above by a constant are exactly the nilpotent ideal extensions of semilattices, Boolean groups and rectangular bands. Trivially, these sequences are polynomially bounded.…”

Section: The Main Resultsmentioning

confidence: 99%

“…Since then, the theory provided many interesting and nice results, for example [1], [2], [3], [16], [18], [19] and [26], just to mention some. Concerning p n -sequences of semigroups and related topics, we have [12], [11], [8], then the characterization of semigroups having sub-exponential (also called log-linear) p n -sequences [9] (which is going to be utilized in the sequel), and also [5], [6], [7], [10] and many others.…”

Section: Introductionmentioning

confidence: 99%

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Finite semigroups with slowly growing p n -sequences

Crvenković¹,

Dolinka²

2000

Algebra Universalis

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The p n -sequence of a semigroup S is said to be polynomially bounded, if there exist a positive constant c and a positive integer r such that the inequality p n (S) ≤ cn r holds for all n ≥ 1. In this paper, we fully describe all finite semigroups having polynomially bounded p n -sequences. First we give a characterization in terms of identities satisfied by these semigroups. In the sequel, this result will allow an insight into the structure of such semigroups. We are going to deal with certain ideals and the construction of ideal extension of semigroups. In addition, we supply an effective procedure for deciding whether a finite semigroup has polynomially bounded p nsequence and give some examples.

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Section: The Main Resultsmentioning

confidence: 76%

Section: The Main Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite semigroups with slowly growing p n -sequences

Crvenković¹,

Dolinka²

2000

Algebra Universalis

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“…Finite semigroups (or, equivalently, finitely generated semigroup varieties) with p n -sequences bounded by a constant were investigated in [4], and that paper provided equational, algorithmic and structural descriptions of such finite semigroups. A careful reading of the proof of Theorem 4.1 of [4] (the equational characterization) shows that removing the finiteness condition from the theorem in question and leaving the rest of its statement unchanged, yields, in fact, the characterization of all (a fortiori locally finite) semigroup varieties (semigroups) with bounded p n -sequences. However, this conclusion can be obtained at this point immediately, by making some minor modifications in the above proof, which we sketch below.…”

Section: Theorem 8 Let V Be a Semigroup Variety Then There Exists Amentioning

confidence: 99%

Semigroup varieties with a small number of term operations

Dolinka

2003

Algebra Universalis

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“…Recently some extremely interesting results concerning semigroups have appeared. In [5] all the finite semigroups with bounded p n -sequences are described as nilpotent extensions of semilattices, Boolean groups and rectangular bands, i.e., the ideal extensions of the semigroups by a nilpotent semigroup. All the finite semigroups with polynomially bounded p n -sequences are characterized in [3].…”

Section: Associative Square Extensionmentioning

confidence: 99%