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A. Moura 《Semigroup Forum》2012,85(1):169-181
Generalizing a property of the pseudovariety of all aperiodic semigroups observed by Tilson, we call E -local a pseudovariety V which satisfies the following property: for a finite semigroup, the subsemigroup generated by its idempotents belongs to V if and only if so do the subsemigroups generated by the idempotents in each of its regular $\mathcal{D}$ -classes. In this paper, we present several sufficient or necessary conditions for a pseudovariety to be E-local or for a pseudoidentity to define an E-local pseudovariety. We also determine several examples of the smallest E-local pseudovariety containing a given pseudovariety. 相似文献
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We show that the pointlike and the idempotent pointlike problems are reducible with respect to natural signatures in the following cases: the pseudovariety of all finite semigroups in which the order of every subgroup is a product of elements of a fixed set \(\pi \) of primes; the pseudovariety of all finite semigroups in which every regular \(\mathcal J\)-class is the product of a rectangular band by a group from a fixed pseudovariety of groups that is reducible for the pointlike problem, respectively graph reducible. Allowing only trivial groups, we obtain \(\omega \)-reducibility of the pointlike and idempotent pointlike problems, respectively for the pseudovarieties of all finite aperiodic semigroups (\(\mathsf{A}\)) and of all finite semigroups in which all regular elements are idempotents (\(\mathsf{DA}\)). 相似文献
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Igor Dolinka 《Semigroup Forum》2012,85(2):244-254
The pseudovariety DA consists of all aperiodic finite monoids all of whose regular -classes are subsemigroups (that is, rectangular subbands); this pseudovariety appears quite frequently in various contexts in finite semigroup theory. In this note we prove that all its members have a log-polynomial free spectrum, thereby making a new step towards proving the Seif conjecture on the dichotomy of free spectra of finite monoids. 相似文献
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It is well known that the pseudovariety \(\mathbf {J}\) of all \(\mathscr {J}\)-trivial monoids is not local, which means that the pseudovariety \(g\mathbf {J}\) of categories generated by \(\mathbf {J}\) is a proper subpseudovariety of the pseudovariety \(\ell \mathbf {J}\) of categories all of whose local monoids belong to \(\mathbf {J}\). In this paper, it is proved that the pseudovariety \(\mathbf {J}\) enjoys the following weaker property. For every prime number p, the pseudovariety \(\ell \mathbf {J}\) is a subpseudovariety of the pseudovariety \(g(\mathbf {J}*\mathbf {Ab}_p)\), where \(\mathbf {Ab}_p\) is the pseudovariety of all elementary abelian p-groups and \(\mathbf {J}*\mathbf {Ab}_p\) is the pseudovariety of monoids generated by the class of all semidirect products of monoids from \(\mathbf {J}\) by groups from \(\mathbf {Ab}_p\). As an application, a new proof of the celebrated equality of pseudovarieties \(\mathbf {PG}=\mathbf {BG}\) is obtained, where \(\mathbf {PG}\) is the pseudovariety of monoids generated by the class of all power monoids of groups and \(\mathbf {BG}\) is the pseudovariety of all block groups. 相似文献
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The graph of an algebra A is the relational structure G(A) in which the relations are the graphs of the basic operations of A. For a class ?? of algebras let G(??)={G(A)∣A∈??}. Assume that ?? is a class of semigroups possessing a nontrivial member with a neutral element and let ? be the universal Horn class generated by G(??). We prove that the Boolean core of ?, i.e., the topological prevariety generated by finite members of ? equipped with the discrete topology, does not admit a first-order axiomatization relative to the class of all Boolean topological structures in the language of ?. We derive analogous results when ?? is a class of monoids or groups with a nontrivial member. 相似文献
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Ben Barber 《Graphs and Combinatorics》2014,30(2):267-274
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Tim Stokes 《Algebra Universalis》2011,66(1-2):85-98
The agreement quasi-order on pairs of (partial) transformations on a set X is defined as follows: ${(f, g) \preceq (h, k)}$ if whenever f, g are defined and agree, so do h, k. We axiomatize function semigroups and monoids equipped with this quasi-order, thereby providing a generalisation of first projection quasi-ordered ${\cap}$ -semigroups of functions. As an application, axiomatizations are obtained for groups and inverse semigroups of injective functions equipped with the quasi-order of fix-set inclusion. All axiomatizations are finite. 相似文献
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Kristian Seip 《Mathematische Zeitschrift》2013,274(3-4):1327-1339
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Juraj Činčura 《Applied Categorical Structures》2013,21(6):671-679
In this paper the structure of hereditary coreflective subcategories in the categories Tych of Tychonoff and ZD of zero-dimensional spaces is studied. It is shown that there are (many) hereditary additive and divisible subcategories in Tych and ZD which are not coreflective. Moreover, if ${\mathcal{A}}$ is an epireflective subcategory of the category Top of topological spaces which is not bireflective and ${\mathcal{B}}$ is an additive and divisible subcategory of ${\mathcal{A}}$ which is not coreflective, then the coreflective hull of ${\mathcal{B}}$ in ${\mathcal{A}}$ is not hereditary. It is also shown, in the case of Tych under Martin’s axiom or under the continuum hypothesis, that if ${\mathcal{B}}$ is a hereditary coreflective subcategory of Tych (ZD), then either the topologies of all spaces belonging to ${\mathcal{B}}$ are closed under countable intersections or it contains all Tychonoff spaces (zero-dimensional spaces) with Ulam nonmeasurable cardinality. 相似文献