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In this paper we give characterizations of topological Clifford semigroups which are embeddable into Tychonoff products of topological semilattices and cones over topological groups. Also we characterize topological Clifford semigroups which embed into compact topological Clifford semigroups. 相似文献
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M. V. Semenova 《Algebra and Logic》2006,45(4):248-253
Repnitskii proved that any lattice embeds in a subsemigroup lattice of some commutative, cancellative, idempotent free semigroup
with unique roots. In that proof, use is made of a result by Bredikhin and Schein stating that any lattice embeds in a suborder
lattice of suitable partial order. Here, we present a direct proof of Repnitskii’s result which is independent of Bredikhin-Schein’s,
thus giving the answer to the question posed by Shevrin and Ovsyannikov.
Supported by INTAS grant No. 03-51-4110; RF Ministry of Education grant No. E02-1.0-32; Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-2112.2003.1; a grant from the Russian Science Support Foundation;
SB RAS Young Researchers Support project No. 11.
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Translated from Algebra i Logika, Vol. 45, No. 4, pp. 436–446, July–August, 2006. 相似文献
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T. Y. Lam 《Proceedings of the American Mathematical Society》2001,129(11):3161-3166
In a tour de force in 1955, S. A. Amitsur classified all finite groups that are embeddable in division rings. In particular, he disproved a conjecture of Herstein which stated that odd-order emdeddable groups were cyclic. The smallest counterexample turned out to be a group of order 63. In this note, we prove a non-embedding result for a class of metacyclic groups, and present an alternative approach to a part of Amitsur's results, with an eye to ``de-mystifying" the order 63 counterexample.
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M. V. Semenova 《Siberian Mathematical Journal》2007,48(1):156-164
We prove that the class of the lattices embeddable into subsemigroup lattices of n-nilpotent semigroups is a finitely based variety for all n < ω. Repnitski? showed that each lattice embeds into the subsemigroup lattice of a commutative nilsemigroup of index 2. In this proof he used a result of Bredikhin and Schein which states that each lattice embeds into the suborder lattices of an appropriate order. We give a direct proof of the Repnitski? result not appealing to the Bredikhin-Schein theorem, so answering a question in a book by Shevrin and Ovsyannikov. 相似文献
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Detlev Poguntke 《Semigroup Forum》1977,15(1):159-167
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梁金玲 《纯粹数学与应用数学》1999,15(2):33-36
讨论了一类群的幂半群的半格分解,得到了最大半格分解的刻划,及有关滤子,完全素理想等一系列结果,作为特例,得到了Putcha.M.S.关于有限群的幂半群的最大半格分解的结论。 相似文献
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We consider α-times integrated C-regularized semigroups, which are a hybrid between semigroups regularized in space (C-semigroups) and integrated semigroups regularized in time. We study the basic properties of these objects, also in absence of exponential boundedness. We discuss their generators and establish an equivalence theorem between existence of integrated regularized semigroups and well-posedness of certain Cauchy problems. We investigate the effect of smoothing regularized semigroups by fractional integration. 相似文献
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Mohan S. Putcha 《Semigroup Forum》1971,3(1):51-57
In this paper we study commutative semigroups whose every homomorphic image in a group is a group. We find that for a commutative
semigroup S, this property is equivalent to S being a union of subsemigroups each of which either has a kernel or else is
isomorphic to one of a sequence T0, T1, T2, ... of explicitly given, countably infinite semigroups without idempotents. Moreover, if S is also finitely generated then
this property is equivalent to S having a kernel. 相似文献