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694
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"... � in terms of idempotent-generated regular semigroup E, with a medial idempotent u, and of the orthodox semigroups with identity S, such that ES ( ) � u E u. In that paper M. Loganathan has also shown, that every regular semigroup S with a medial idempotent u, can be described in terms of the subse ..."
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� in terms of idempotent-generated regular semigroup E, with a medial idempotent u, and of the orthodox semigroups with identity S, such that ES ( ) � u E u. In that paper M. Loganathan has also shown, that every regular semigroup S with a medial idempotent u, can be described in terms
Depth of idempotent-generated subsemigroups of a regular ring
- MR 90h:16021. Zbl 653.16006
, 1989
"... If S is an idempotent-generated semigroup, its depth is the minimum number of idempotents needed to express a general element as a product of idempo tents. Here we study the depth of 5 where 5 is the semigroup generated by all the idempotents of a von Neumann regular ring R, and the depth of various ..."
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If S is an idempotent-generated semigroup, its depth is the minimum number of idempotents needed to express a general element as a product of idempo tents. Here we study the depth of 5 where 5 is the semigroup generated by all the idempotents of a von Neumann regular ring R, and the depth
IDEMPOTENT-GENERATED SEMIGROUPS AND PSEUDOVARIETIES
"... Abstract. The operator which constructs the pseudovariety generated by the idempotent-generated semigroups of a given pseudovariety is investigated. Several relevant examples of pseudovarieties generated by their idempotentgenerated elements are given as well as some properties of this operator. Par ..."
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Abstract. The operator which constructs the pseudovariety generated by the idempotent-generated semigroups of a given pseudovariety is investigated. Several relevant examples of pseudovarieties generated by their idempotentgenerated elements are given as well as some properties of this operator
ON SEMIGROUPS WHOSE IDEMPOTENT-GENERATED SUBSEMIGROUP IS APERIODIC
, 2004
"... We show that if S is a finite semigroup with aperiodic idempotent-generated subsemigroup and H is a pseudovariety of groups, then the sequence of iterated H-kernels of S stops at the idempotent-generated subsemigroup if and only if each subgroup of S belongs to the wreath product closure of H. Appli ..."
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We show that if S is a finite semigroup with aperiodic idempotent-generated subsemigroup and H is a pseudovariety of groups, then the sequence of iterated H-kernels of S stops at the idempotent-generated subsemigroup if and only if each subgroup of S belongs to the wreath product closure of H
GROUPS THAT TOGETHER WITH ANY TRANSFORMATION GENERATE REGULAR SEMIGROUPS OR IDEMPOTENT GENERATED SEMIGROUPS
"... Abstract. Let a be a non-invertible transformation of a finite set and let G be a group of permutations on that same set. Then 〈 G, a 〉 \ G is a subsemigroup, consisting of all non-invertible transformations, in the semigroup generated by G and a. Likewise, the conjugates a g = g −1 ag of a by elem ..."
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Cited by 5 (4 self)
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by elements g ∈ G generate a semigroup denoted 〈a g | g ∈ G〉. We classify the finite permutation groups G on a finite set X such that the semigroups 〈G, a〉, 〈G, a〉\G, and 〈a g | g ∈ G 〉 are regular for all transformations of X. We also classify the permutation groups G on a finite set X
Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid
, 2012
"... Let Tn be the full transformation semigroup of all mappings from the set {1,..., n} to itself under composition. Let E = E(Tn) denote the set of idempotents of Tn and let e ∈ E be an arbitrary idempotent satisfying |im (e) | = r n − 2. We prove that the maximal subgroup of the free idempotent-gene ..."
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Cited by 5 (2 self)
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Let Tn be the full transformation semigroup of all mappings from the set {1,..., n} to itself under composition. Let E = E(Tn) denote the set of idempotents of Tn and let e ∈ E be an arbitrary idempotent satisfying |im (e) | = r n − 2. We prove that the maximal subgroup of the free idempotent-generated
On Maximal Subgroups of Free Idempotent Generated Semigroups
, 2009
"... We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free ..."
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regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free regular idempotent generated semigroup arising from a finite regular semigroup. 2000 Mathematics Subject Classification: 20M05, 20F05. 1 Introduction and summary of results Let S be a semigroup, and let E = E
On Free Products of Completely Regular Semigroups
, 1993
"... The free product CR S i of an arbitrary family of disjoint completely simple semigroups fS i g i2I , within the variety CR of completely regular semigroups, is described by means of a theorem generalizing that of Ka dourek and Pol'ak for free completely regular semigroups. A notable cons ..."
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Cited by 1 (1 self)
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consequence of the description is that all maximal subgroups of CR S i are free, except for those in the factors S i themselves. The general theorem simplifies in the case of free CR-products of groups and, in particular, free idempotent-generated completely regular semigroups. 1980 Mathematics Subject
Subgroups of free idempotent generated semigroups need not be free
- J. Algebra
"... Let S be a semigroup with set E(S) of idempotents, and let 〈E(S) 〉 denote the subsemigroup of S generated by E(S). We say that S is an idempotent generated semigroup if S = 〈E(S)〉. Idempotent generated semigroups have received considerable attention in the literature. For example, an early result ..."
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Cited by 17 (0 self)
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Let S be a semigroup with set E(S) of idempotents, and let 〈E(S) 〉 denote the subsemigroup of S generated by E(S). We say that S is an idempotent generated semigroup if S = 〈E(S)〉. Idempotent generated semigroups have received considerable attention in the literature. For example, an early result
Results 1 - 10
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694
