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Decidable and undecidable problems related to completely 0simple semigroups
, 1996
"... The undecidable problems of the title are concerned with the question: is a given finite semigroup embeddable in a given type of completely 0simple semigroups? It is shown, for example, that the embeddability of a (finite) 3nilpotent semigroup in a finite completely 0simple semigroup is decidabl ..."
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The undecidable problems of the title are concerned with the question: is a given finite semigroup embeddable in a given type of completely 0simple semigroups? It is shown, for example, that the embeddability of a (finite) 3nilpotent semigroup in a finite completely 0simple semigroup
ON THE NILPOTENCY IN SEMIGROUPS
"... This paper is an extension of the results of papers [3] and [5]. The first three theorems of this paper are extensions of the first three theorems of the paper [3] and the fourth theorem of this paper is an extension of the theorem of paper [5]. We introduce three kinds of nilpotency and consider in ..."
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This paper is an extension of the results of papers [3] and [5]. The first three theorems of this paper are extensions of the first three theorems of the paper [3] and the fourth theorem of this paper is an extension of the theorem of paper [5]. We introduce three kinds of nilpotency and consider
HOUSTON JOURNAL OF MATHEMATICS, Volume 4. No. 3, 19?8. A CLASS OF NILPOTENT SEMIGROUPS ON HILBERT SPACE
"... extensive. Various special classes of such semigroups have, to varying degrees, been analyzed and characterized • such as isometric ([1] • [6]), subnormal ([5]), and partially isometric ([3], [8], [9]) semigroups. In his analysis of partially isometric semigroups L. J. Wallen paid special attention ..."
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extensive. Various special classes of such semigroups have, to varying degrees, been analyzed and characterized • such as isometric ([1] • [6]), subnormal ([5]), and partially isometric ([3], [8], [9]) semigroups. In his analysis of partially isometric semigroups L. J. Wallen paid special attention
On finitely related semigroups
, 2012
"... 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, 3nilpotent monoids, regular bands, semigroups with a single idemp ..."
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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, 3nilpotent monoids, regular bands, semigroups with a single
A CONSTRUCTION OF COMMUTATIVE NILPOTENT Semigroups
, 2013
"... In this paper, we construct nilpotent semigroups S such that Sn = {0}, Sn−1 6 = {0} and Γ(S) is a refinement of the star graph K1,n−3 with center c together with finitely many or infinitely many end vertices adjacent to c, for each finite positive integer n ≥ 5. We also give counting formulae to ca ..."
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In this paper, we construct nilpotent semigroups S such that Sn = {0}, Sn−1 6 = {0} and Γ(S) is a refinement of the star graph K1,n−3 with center c together with finitely many or infinitely many end vertices adjacent to c, for each finite positive integer n ≥ 5. We also give counting formulae
Coclass theory for nilpotent semigroups via their associated algebras
, 2012
"... Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in that we additionally use certain algebras associated to the ..."
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Cited by 1 (0 self)
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0 and 1. Computational experiments suggest that the conjectures also hold for the nilpotent semigroups of coclass 2 and 3. 1
More non semigroup Lie gradings
"... Abstract. This note is devoted to the construction of two very easy examples, of respective dimensions 4 and 6, of graded Lie algebras whose grading is not given by a semigroup, the latter one being a semisimple algebra. It is shown that 4 is the minimal possible dimension. Patera and Zassenhaus [PZ ..."
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nilpotent Lie algebra of dimension 16 was defined, with a grading not given by an abelian semigroup. This example came as a surprise (see [Svo08]), but its difficulty may give the impression that this is a rare phenomenon. The purpose of this note is to give two more counterexamples that show that non
Reducibility of semigroups and nilpotent commutators with idempotents of rank two
, 2010
"... Let f be a noncommutative polynomial in two variables. Let S be a multiplicative semigroup of linear operators on a finitedimensional vector space and T a fixed linear operator such that f(T, S) is nilpotent for all S in S. In [3] the authors propose questions, what one can say about the invariant ..."
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Let f be a noncommutative polynomial in two variables. Let S be a multiplicative semigroup of linear operators on a finitedimensional vector space and T a fixed linear operator such that f(T, S) is nilpotent for all S in S. In [3] the authors propose questions, what one can say about the invariant
Algorithmic Problems for Finite Groups and Finite 0Simple Semigroups
, 1996
"... It is shown that the embeddability of a finite 4nilpotent semigroup into a 0simple finite semigroup with maximal groups from a pseudovariety V is decidable if and only if the universal theory of the class V is decidable. We show that it is impossible to replace 4 by 3 in this statement. We also sho ..."
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It is shown that the embeddability of a finite 4nilpotent semigroup into a 0simple finite semigroup with maximal groups from a pseudovariety V is decidable if and only if the universal theory of the class V is decidable. We show that it is impossible to replace 4 by 3 in this statement. We also
Results 1  10
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