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S. A. Shkarin 《Mathematical Notes》2000,67(4):534-540
Both the existence and the nonexistence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison class) are compatible with the ZFC axioms of set theory. Translated fromMaternaticheskie Zametki, Vol. 67, No. 4, pp. 629–637, April, 2000. 相似文献
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A. A. Husainov 《Siberian Mathematical Journal》1994,35(5):1040-1051
Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 35, No. 5, pp. 1171–1184, September–October, 1994. 相似文献
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V. V. Doroshenko 《Ukrainian Mathematical Journal》2009,61(6):859-872
We consider semigroups of endomorphisms of linearly ordered sets ℕ and ℤ and their subsemigroups of cofinite endomorphisms.
We study the Green relations, groups of automorphisms, conjugacy, centralizers of elements, growth, and free subsemigroups
in these subgroups. 相似文献
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Manfred Droste 《Order》1985,2(3):291-319
Using combinatorial and model-theoretic means, we examine the structure of normal subgroup lattices N(A()) of 2-transitive automorphism groups A() of infinite linearly ordered sets (, ). Certain natural sublattices of N(A()) are shown to be Stone algebras, and several first order properties of their dense and dually dense elements are characterized within the Dedekind-completion
of (, ). As a consequence, A() has either precisely 5 or at least 221 (even maximal) normal subgroups, and various other group- and lattice-theoretic results follow. 相似文献
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It is well known that infinite minimal sets for continuous functions on the interval are Cantor sets; that is, compact zero
dimensional metrizable sets without isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat Chaos
13:1665–1671, 2003) that infinite minimal sets for continuous functions on connected linearly ordered spaces enjoy the same
properties as Cantor sets except that they can fail to be metrizable. However, no examples of such subsets have been known.
In this note we construct, in ZFC, non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces.
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N. K. Vereshchagin 《Mathematical Notes》1990,47(5):444-449
Translated from Matematicheskie Zametki, Vol. 47, No. 5, pp. 31–38, May, 1990. 相似文献
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The Kopytov order for any algebras over a field is considered. Necessary and sufficient conditions for an algebra to be a linearly ordered algebra are presented. Some results concerning the properties of ideals of linearly ordered algebras are obtained. Some examples of algebras with the Kopytov order are described. The Kopytov order for these examples induces the order on other algebraic objects. 相似文献
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We give a complete classification and construction of all normal subgroup lattices of 2-transitive automorphism groupsA(Ω) of linearly ordered sets (Ω, ≦). We also show that in each of these normal subgroup lattices, the partially ordered subset
of all those elements which are finitely generated as normal subgroups forms a lattice which is closed under even countably-infinite
intersections, and we derive several further group-theoretical consequences from our classification.
This research was supported by an award from the Minerva-Stiftung, München. The work was done during a stay of the first-named
author at The Hebrew University of Jerusalem in fall 1982. He would like to thank his colleagues in Jerusalem for their hospitality
and a wonderful time. 相似文献
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A bisector of two sets is the set of points equidistant form them. Bisectors arise naturally in several areas of computational
geometry. We show that bisectors of weakly linearly separable sets inE
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have many properties of interest. Among these, the bisector of a restricted class of linearly separated sets is a homeomorphic
image of the linear separator. We also give necessary and sufficient conditions for the existence of a particular continuous
map from (a portion of) any linear separator to the bisector. 相似文献
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We introduce the class of lineal rings, defined by the property that the lattice of right annihilators is linearly ordered. We obtain results on the structure of these rings, their ideals, and important radicals; for instance, we show that the lower and upper nilradicals of these rings coincide. We also obtain an affirmative answer to the Köthe Conjecture for this class of rings. We study the relationships between lineal rings, distributive rings, Bézout rings, strongly prime rings, and Armendariz rings. In particular, we show that lineal rings need not be Armendariz, but they fall not far short. 相似文献