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1.
This article presents some conditions, expressed in terms of the inclusion and exclusion of certain small semigroups, that are related to a Rees-Sushkevich variety being generated by completely 0-simple or completely simple semigroups.  相似文献   

2.
Denote by RS n the variety generated by all completely 0-simple semigroups over groups of exponent dividing n. Subvarieties of RS n are called Rees-Sushkevich varieties and those that are generated by completely simple or completely 0-simple semigroups are said to be exact. For each positive integer m, define C m RS n to be the class of all semigroups S in RS n with the property that if the product of m idempotents of S belongs to some subgroup of S, then the product belongs to the center of that subgroup. The classes C m RS n constitute varieties that are the main object of investigation in this article. It is shown that a sublattice of exact subvarieties of C 2 RS n is isomorphic to the direct product of a three-element chain with the lattice of central completely simple semigroup varieties over groups of exponent dividing n. In the main result, this isomorphism is extended to include those exact varieties for which the intersection of the core with any subgroup, if nonempty, is contained in the center of that subgroup. The equational property of the varieties C m RS n is also addressed. For any fixed n ≥ 2, it is shown that although the varieties C m RS n , where m = 1, 2, ... , are all finitely based, their complete intersection (denoted by C RS n ) is non-finitely based. Further, the variety C RS n contains a continuum of ultimately incomparable infinite sequences of finitely generated exact subvarieties that are alternately finitely based and non-finitely based. Received October 29, 2003; accepted in final form February 11, 2007.  相似文献   

3.
In a previous paper, the author showed how to associate a completely 0-simple semigroup with a connected bipartite graph containing labelled edges. In the main theorem, it is shown how these fundamental semigroups can be used to describe the regular principal factors of the free objects in certain Rees-Sushkevich varieties, namely, the varieties of semigroups that are generated by all completely 0-simple semigroups over groups in a variety of finite exponent. This approach is then used to solve the word problem for each of these varieties for which the corresponding group variety has solvable word problem.  相似文献   

4.
Zappa–Szép products arise when an algebraic structure has the property that every element has a unique decomposition as a product of elements from two given substructures. They may also be constructed from actions of two structures on one another, satisfying axioms first formulated by G. Zappa, and have a natural interpretation within automata theory. We study Zappa–Szép products arising from actions of a group and a band, and study the structure of the semigroup that results. When the band is a semilattice, the Zappa–Szép product is orthodox and ℒ-unipotent. We relate the construction (via automata theory) to the λ-semidirect product of inverse semigroups devised by Billhardt.  相似文献   

5.
6.
We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary and sufficient conditions for the existence of equivalences between the twisted derived categories of two Kummer surfaces in terms of Hodge isometries between the generalized transcendental lattices of the corresponding abelian surfaces.   相似文献   

7.
8.
Following W. Taylor, we define an identity to be hypersatisfied by a variety V iff, whenever the operation symbols of V are replaced by arbitrary terms (of appropriate arity) in the operations of V, then the resulting identity is satisfied by V in the usual sense. Whenever the identity is hypersatisfied by a variety V, we shall say that is a hyperidentity of V, or a V hyperidentity. When the terms being substituted are restricted to a submonoid M of all the possible choices, is called an M-hyperidentity, and a variety V is M-solid if each identity is an M-hyperidentity. In this paper we examine the solid varieties whose identities are lattice M-hyperidentities. The M-solid varieties generated by the variety of lattices in this way provide new insight on the construction and representation of various known classes of non-commutative lattices. Received October 8, 1999; accepted in final form March 22, 2000.  相似文献   

9.
10.
We derive a lower bound of the generalized Hamming weights of the codes over affine varieties, which are defined by appropriate sequences of rational polynomials over varieties.  相似文献   

11.
Let be the flag variety of a complex semi-simple group G, let H be an algebraic subgroup of G acting on with finitely many orbits, and let V be an H-orbit closure in . Expanding the cohomology class of V in the basis of Schubert classes defines a union V0 of Schubert varieties in with positive multiplicities. If G is simply-laced, we show that these multiplicities are equal to the same power of 2. For arbitrary G, we show that V0 is connected in codimension 1. If moreover all multiplicities are 1, we show that the singularities of V are rational and we construct a flat degeneration of V to V0 in . Thus, for any effective line bundle L on , the restriction map is surjective, and for all . Received: April 17, 2000  相似文献   

12.
We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, if the barycenter of the associated reflexive polytope is zero. Furthermore a sharp bound on the dimension of the reductive automorphism group of a complete toric variety is proven by studying the set of Demazure roots.  相似文献   

13.
In this paper, we study the irreducible decompositions of determinantal varieties of matrices given by rank conditions on upper left submatrices. Using the concept of essential rank function and the Ehresmann partial order on the set of all simple matrices, we design an algorithm to write a determinantal variety as a union of its irreducible components. This solves a problem raised by B. Sturmfels.   相似文献   

14.
We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complexIH T * (X)⊗H*(T). We also describe the weight filtration inIH *(X). Supported by KBN 2P03A 00218 grant. I thank, Institute of Mathematics, Polish Academy of Science for hospitality.  相似文献   

15.
Andrzej Weber 《Topology》2004,43(3):635-644
We show that for a complete complex algebraic variety the pure term of the weight filtration in homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce image homology for noncomplete varieties.  相似文献   

16.
We describe the construction of a class of toric varieties as spectra of homogeneous prime ideals.   相似文献   

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18.
Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of “smaller” flag varieties. We consider the type A partial flag variety and find that its cohomology exhibits a Horn recursion on a certain deformation of the cup product defined by Belkale and Kumar (Invent. Math. 166:185–228, 2006). We also show that if a product of Schubert classes is non-vanishing on this deformation, then the associated structure constant can be written in terms of structure constants coming from induced Grassmannians.  相似文献   

19.
As a piecewise polynomial with a certain smoothness, the spline plays an important role in computational geometry. The algebraic variety is the most important subject in classical algebraic geometry. As the zero set of multivariate splines, the piecewise algebraic variety is a generalization of the algebraic variety. In this paper, the correspondence between piecewise algebraic varieties and spline ideals is discussed. Furthermore, Hilbert’s Nullstellensatz for the piecewise algebraic variety is also studied.  相似文献   

20.
In this paper we recall basic properties of complex Shimura varieties and show that they actually characterize them. This characterization immediately implies the explicit form of Kazhdan's theorem on the conjugation of Shimura varieties. It also implies the existence of unique equivariant models over the reflex field of Shimura varieties corresponding to adjoint groups and the existence of a p-adic uniformization of certain unitary Shimura varieties. In the appendix we give a modern formulation and a proof of Weil's descent theorem.  相似文献   

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