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Decidable and undecidable problems related to completely 0-simple 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 0-simple semigroups? It is shown, for example, that the embeddability of a (finite) 3-nilpotent semigroup in a finite completely 0-simple semigroup is decidabl ..."
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is decidable yet such embeddability is undecidable for a (finite) 4-nilpotent semigroup. As well the membership of the pseudovariety generated by finite completely 0-simple semigroups (or alternatively by finite Brandt semigroups) over groups from a pseudovariety of groups with decidable membership is shown
Algorithmic Problems for Finite Groups and Finite 0-Simple Semigroups
, 1996
"... It is shown that the embeddability of a finite 4-nilpotent 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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Cited by 1 (0 self)
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It is shown that the embeddability of a finite 4-nilpotent 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
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 ..."
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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Cited by 2 (1 self)
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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
Solvable groups of exponential growth and HNN extensions
, 1999
"... An extraordinary theorem of Gromov, [4], characterizes the finitely generated groups of polynomial growth; a group has polynomial growth iff it is nilpotent by finite. This theorem went a long way from its roots in the class of discrete subgroups of solvable Lie groups. Wolf, [11], proved that a pol ..."
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Cited by 3 (1 self)
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An extraordinary theorem of Gromov, [4], characterizes the finitely generated groups of polynomial growth; a group has polynomial growth iff it is nilpotent by finite. This theorem went a long way from its roots in the class of discrete subgroups of solvable Lie groups. Wolf, [11], proved that a
Let ∆ = −
"... Abstract. Let G be a connected Lie group of polynomial growth. We consider m-th order subelliptic differential operators H on G, the semigroups St = e −tH and the corresponding heat kernels Kt. For a large class of H with m> 4 we demonstrate equivalence between the existence of Gaussian bounds on ..."
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Abstract. Let G be a connected Lie group of polynomial growth. We consider m-th order subelliptic differential operators H on G, the semigroups St = e −tH and the corresponding heat kernels Kt. For a large class of H with m> 4 we demonstrate equivalence between the existence of Gaussian bounds
References
"... Let R be an associative ring. The set of all elements of R forms a monoid with the neutral element 0 from R under the circle, or star multiplication r · s = r + s + rs. The monoid of elements of R under this operation is called the adjoint semigroup of R, and the group of its invertible elements is ..."
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of their adjoint group being their subalgebras. [2] deals with p-groups that can occur as the adjoint group of low-dimensional nilpotent p-algebras, and [7] is focused on adjoint groups with a small number of generators. For further results see also [3, 4, 5]. Motivated by these works, we suggest a computational
AN ANSWER TO A QUESTION OF KEGEL ON SUMS OF RINGS
"... ABSTRACT. We construct a ring R which is a sum of two subrings A and B such that the Levitzki radical of R does not contain any of the hyperannihilators of A and B.This answers an open question asked by Kegel in 1964. Kegel [6] proved that a ring is nilpotent if it is a sum of two nilpotent subrings ..."
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ABSTRACT. We construct a ring R which is a sum of two subrings A and B such that the Levitzki radical of R does not contain any of the hyperannihilators of A and B.This answers an open question asked by Kegel in 1964. Kegel [6] proved that a ring is nilpotent if it is a sum of two nilpotent
