On C*-quasiregular semigroups *

In this paper, we introduce an important subclass of quasiregular semigroups, namely the class of C^*-quasiregular semigroups. This class of semigroups contains the classes of Clifford semigroups, quasi Clifford semigroups, C-quasiregular semigroups and their generalizations as its subclasses. Some characterization theorems for such semigroups are obtained. The structure of this kind of quasiregular semigroups is investigated by using the generalized ?-product of some semigroups on a semilattice Y. Construction techniques of such classes of semigroups are particularly demonstrated.     

由格蕴涵代数诱导的伴随半群

给出由格蕴涵代数诱导出的伴随半群及有关概念 ,详细讨论伴随半群中的元素即格蕴涵代数的左映射的性质 ,得到它们的几个等价条件。最后讨论由格蕴涵代数诱导的两个双格半群与伴随半群之间的关系 ,并证明这些半群是幂等的当且仅当它们是由格 H蕴涵代数所诱导     

Semigroups of isometries,Toeplitz algebras and twisted crossed products

We study theC ^*-algebras generated by projective isometric representations of semigroups, using a dilation theorem and the stucture theory of twisted crossed products. These algebras include the Toeplitz algebras of noncommutative tori recently studied by Ji, and similar algebras associated to the twisted group algebras of other groups such as the integer Heisenberg group.     

Duals and topological center of a class of matrix algebras with applications

We characterize the topological center of a class of matrix algebras, which are called -Munn algebras. This involves a characterization of Arens regular semigroup algebras for a large class of semigroups, which is an extension of Young's Theorem for semigroups. We show by some counter examples that only up to a certain extent Young's Theorem can be generalized.

     

Fixed point property for Banach algebras associated to locally compact groups

In this paper we investigate when various Banach algebras associated to a locally compact group G have the weak or weak^∗ fixed point property for left reversible semigroups. We proved, for example, that if G is a separable locally compact group with a compact neighborhood of the identity invariant under inner automorphisms, then the Fourier-Stieltjes algebra of G has the weak^∗ fixed point property for left reversible semigroups if and only if G is compact. This generalizes a classical result of T.C. Lim for the case when G is the circle group T.     

Semigroup C⁎-algebras and amenability of semigroups

We construct reduced and full semigroup C^?-algebras for left cancellative semigroups. Our new construction covers particular cases already considered by A. Nica and also Toeplitz algebras attached to rings of integers in number fields due to J. Cuntz. Moreover, we show how (left) amenability of semigroups can be expressed in terms of these semigroup C^?-algebras in analogy to the group case.     

Ideals and Representations of Certain Semigroup Algebras

We characterize various types of ideals in ¹-Munn algebras with a bounded approximate identity, in terms of the ideals of their underlying algebras. Moreover, we show the correspondence between different types of *-representations of ¹-Munn algebras and *-representations of their underlying algebras. In the context of semigroup algebras, .rst we prove the conjecture which was proposed in [8]. Then we apply the results of the first part to build various representations of unital semigroup algebras of completely 0-simple inverse semigroups. This generalizes some of the Barnes results [1] with different and much shorter proofs.     

Schur–Weyl dualities for symmetric inverse semigroups

We obtain Schur–Weyl dualities in which the algebras, acting on both sides, are semigroup algebras of various symmetric inverse semigroups and their deformations.     

FI代数,BCK代数与关联半群

文献［１］讨论了Ｆｕｚｚｙ蕴涵代数（简称为ＦＩ代数）与ＭＶ代数、格蕴涵代数之间的关系,本文进一步讨论了ＦＩ代数与有界关联ＢＣＫ代数、关联半群的联系,并应用ＦＩ代数方法简化了ＢＣＫ代数中某些定理的证明。     

On a Characterization of Monounary Algebras by their Endomorphism Semigroups

A class of infinite monounary algebras without cyclic elements and such that the operations on these algebras are surjective is considered. It is proved that monounary algebras of this class are determined up to an isomorphism by their endomorphism semigroups.     

The Semigroup Characterizations of Positive Implicative BCK—algebras

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ，，０）ｏｆｔｙｐｅ（２，０）ｗｉｔｈｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉ－ｔｉｏｎｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｉｍｐｌｉｅｓｘ＝ｙ．ＩｆａＢＣＩ－ａｌｇｅｂｒａ（Ｘ，，０）ｓａｔｉｓｆｉｅｓ（５）０ｘ＝０．ｔｈｅｎｉｔｉｓｃａｌｌｅｄａＢＣＫ－ａｌｇｅｂｒａ．ＩｎａＢＣＩ－ａｌｇｅｂｒａ，ｔｈｅｆ…     

On the structure of rotation-invariant semigroups

 We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows from their other axioms. Received: 7 January 2002 / Revised version: 4 April 2002 / Published online: 19 December 2002 RID="*" ID="*" Supported by the National Scientific Research Fund Hungary (OTKA F/032782). Mathematics Subject Classification (2000): 20M14, 06F05 Key words or phrases: Residuated lattice – Conjunction for non-classical logics     

关于两类特殊的代数

本文对泛代数中两类代作了一些研究，得到一些结果，并且讨论了这两类代数在半群中的应用。     

Semigroups satisfying (xy)m = xmym

In this paper we characterize Archimedean semigroups with idempotents satisfying (xy)^m = x^my^m as exactly those semigroups which are a retract extension of a completely simple semigroup satisfying (xy)^m = x^my^m by a nil semigroup satisfying (xy)^m = x^my^m. Regular semigroups satisfying (xy)² = x²y² are exactly those semigroups which are a spined product of a band and a semigroup which is a semilattice of Abelian groups. A semigroup which is a nil extension of a regular semigroup satisfies (xy)² = x²y² if and only if it is a retract extension of a regular semigroup satisfying (xy)² = x²y² by a nil semigroup satisfying (xy)² = x²y²     

Radicals of some semigroup algebras

In this paper we seek to determine the Jacobson radical of certain algebras based on semigroups, and in particular on the semigroups (βS,□), where S is a cancellative, countable, abelian semigroup and βS is its Stone–?ech semigroup compactification. In particular, we wish to determine the radical of ? ^?1(β?).     

强P-正则半群的一个构造

本文研究了强P-正则半群的结构.利用正则*-半群和一族满足某种条件的映射给出了强P-正则半群的一个构造,推广和丰富了相关文献中纯正半群的结果.     

Inner Homomorphisms and Positive-Conditional Terms

We establish the criterion for two finite or uniformly locally finite algebras of a finite signature to be positive-conditionally rational equivalent (in terms of semigroups of inner homomorphisms of these algebras) and the criterion for two finite algebras to be strongly similar (in terms of expanded semigroups of inner homomorphisms of those algebras).     

Congruences on ternary semigroups

We study ternary semigroups as universal algebras with one associative operation. We investigate their algebraic structure and associated representations. Results for congruences of ternary semigroups generated by binary relations are presented.Published in Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 544–559, April, 2004.     

Radical of weakly ordered semigroup algebras

We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras. This generalizes some results on left regular bands and on 0- Hecke algebras.     

The Hopf Structure of Some Dual Operator Algebras

We study the Hopf structure of a class of dual operator algebras corresponding to certain semigroups. This class of algebras arises in dilation theory, and includes the noncommutative analytic Toeplitz algebra and the multiplier algebra of the Drury–Arveson space, which correspond to the free semigroup and the free commutative semigroup respectively. The preduals of the algebras in this class naturally form Hopf (convolution) algebras. The original algebras and their preduals form (non-self-adjoint) dual Hopf algebras in the sense of Effros and Ruan. We study these algebras from this perspective, and obtain a number of results about their structure.