共查询到20条相似文献,搜索用时 15 毫秒
1.
Nathaniel Knox 《Semigroup Forum》1978,16(1):345-354
In this paper the inverse hull of the free semigroup on a non-empty set X is characterized. It is shown that if FO is a certain semilattice and (G,*) is the free group on X, then is isomorphic to a Rees factor semigroup of a subsemigroup of (FO x G, #), where (A,w)#(B,u) = ((A*w B)*w–1, w*u). Several properties of , including Green's relations on are also determined. 相似文献
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The translational hull of an adequate semigroup 总被引:2,自引:0,他引:2
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Semigroup Forum - We prove that the forgetful functor from the category of Boolean inverse semigroups to the category of inverse semigroups with zero has a left adjoint. This left adjoint is what... 相似文献
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This paper is a contribution to the development of the theory of representations of inverse semigroups in toposes. It continues the work initiated by Funk and Hofstra (Theory Appl Categ 24(7):117–147, 2010). For the topos of sets, we show that torsion-free functors on Loganathan’s category L(S) of an inverse semigroup S are equivalent to a special class of non-strict representations of S, which we call connected. We show that the latter representations form a proper coreflective subcategory of the category of all non-strict representations of S. We describe the correspondence between directed and pullback preserving functors on L(S) and transitive and effective representations of S, as well as between filtered such functors and universal representations introduced by Lawson, Margolis and Steinberg. We propose a definition of a universal representation, or, equivalently, an S-torsor, of an inverse semigroup S in the topos of sheaves \({\mathsf {Sh}}(X)\) on a topological space X. We prove that the category of filtered functors from L(S) to the topos \({\mathsf {Sh}}(X)\) is equivalent to the category of universal representations of S in \({\mathsf {Sh}}(X)\). We finally propose a definition of an inverse semigroup action in an arbitrary Grothendieck topos, which arises from a functor on L(S). 相似文献
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认为S的每个元素都诱导了S-系上的一个一元运算,因此S-系是有限代数,泛代数中的所有概念都是适用的.定义了S-系的可半格化子集和S-系的子集的面,构建了逆半群上的S一系的内射壳.推广了有关文献中的结果. 相似文献
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John K. Luedeman 《Semigroup Forum》1974,9(1):76-83
A generalized translational hull of a semigroup is constructed. Its relationship to (S) and Q(S) as well as its homological properties are demonstrated. 相似文献
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Recep Korkmaz 《Semigroup Forum》2009,78(3):528-535
In this paper we study dense inverse subsemigroups of topological inverse semigroups. We construct a topological inverse semigroup
from a semilattice. Finally, we give two examples of the closure of B
( −∞, ∞ )1, a topological inverse semigroup obtained by starting with the real numbers as a semilattice with the operation a
∨
b=sup{a,b}.
The author would like to thank to the referee for useful suggestions. 相似文献
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Semigroup Forum - For an inverse semigroup S with the set of idempotents E, we find necessary and sufficient conditions for the Fourier algebra A(S) to be module amenable, module character... 相似文献
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Semigroup Forum - After reviewing aspects of the development of inverse semigroup theory, we describe an approach to studying them which views them as ‘non-commutative meet... 相似文献
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The translational hull of a strongly right type-A semigroup 总被引:2,自引:0,他引:2
It is proved that the translational hull of a strongly right type-A (C-rpp) semigroup is itself a strongly right type-A(C-rpp) semigroup. 相似文献
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In this paper, the translational hull of a type B semigroup is considered. We prove that the translational hull of a type B
semigroup is itself a type B semigroup, and give some properties and characterizations of the translational hulls of such
semigroups. Moreover, we consider the translational hulls of some special type B semigroups. These results strengthen the
results of Fountain and Lawson (Semigroup Forum 32:79–86, 1985) on adequate semigroups. Finally, we give a new proof of a problem posted by Petrich on translational hulls of inverse semigroups
in Petrich (Inverse Semigroups, Wiley, New York, 1984). 相似文献
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Lucyna Kabza 《代数通讯》2013,41(14):5419-5435
Let G be a group and S an inverse semigroup of endomorphisms of G. The simplicity of the centralizer near- ring MS(G) = {fε M(G)‖foα = αo f, ?αεS} is characterized. The necessary and sufficient conditions are given for simplicity of Ms(G) in terms of the structure of G and S. 相似文献
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I. Lie 《Journal of Mathematical Sciences》1978,9(3):322-331
The Burnside algebra for a finite inverse semigroup over a field is considered (the analog of the Grothendieck algebra). The conditions for the algebra to be Frobenius are investigated. It is shown that, if all the subgroups in the semigroup are commutative, then its Burnside algebra is Frobenius if and only if the order of any maximal subgroup is not divisible by the square of the field characteristic.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 46, pp. 41–52, 1974. 相似文献
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For an amenable inverse semigroup S with the set of idempotents E and a minimal idempotent, we explicitly construct a contractive and positive module operator virtual diagonal on the Fourier algebra A(S), as a completely contractive Banach algebra and operator module over \(\ell ^1(E)\). This generalizes a well known result of Zhong-Jin Ruan on operator amenability of the Fourier algebra of a (discrete) group Ruan (Am J Math 117:1449–1474, 1995). 相似文献
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