共查询到20条相似文献,搜索用时 12 毫秒
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.
Norman R. Reilly 《Semigroup Forum》2013,86(1):162-182
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.
Jeremy L. Martin 《Transactions of the American Mathematical Society》2003,355(10):4151-4169
6.
Paolo Stellari 《Mathematische Zeitschrift》2007,256(2):425-441
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.
《Journal of Pure and Applied Algebra》2022,226(6):106969
We investigate the secant dimensions and the identifiability of flag varieties parametrizing flags of subspaces of a fixed vector space. We give numerical conditions ensuring that secant varieties of flag varieties have the expected dimension, and that a general point on these secant varieties is identifiable. 相似文献
8.
9.
Elena Rubei 《Transactions of the American Mathematical Society》2000,352(6):2569-2579
In this paper we prove the following result: Let be a complex torus and a normally generated line bundle on ; then, for every , the line bundle satisfies Property of Green-Lazarsfeld.
10.
11.
WU Xinwen 《中国科学A辑(英文版)》2000,43(2):141-148
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
12.
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
13.
B. A. Sethuraman 《Proceedings of the American Mathematical Society》1998,126(1):9-14
Let , where is a prime, and . In , let be the variety defined by . We show that any subvariety of of codimension less than must have degree a multiple of . We also show that the bounds on the codimension in our results are strict by exhibiting subvarieties of the appropriate codimension whose degrees are prime to .
14.
M. Brion 《Commentarii Mathematici Helvetici》2001,76(2):263-299
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
15.
Benjamin Nill 《Mathematische Zeitschrift》2006,252(4):767-786
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
16.
Ernesto C. Mistretta 《Mathematische Nachrichten》2020,293(11):2175-2186
A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational characterization of abelian varieties. In particular we prove that, under the conjectures of the Minimal Model Program, a smooth projective variety is birational to an abelian variety if and only if it has Kodaira dimension 0 and some symmetric power of its cotangent sheaf is generically generated by its global sections. 相似文献
17.
18.
N. Naumann 《Transactions of the American Mathematical Society》2007,359(4):1653-1683
We give sufficient cohomological criteria for the classes of given varieties over a field to be algebraically independent in the Grothendieck ring of varieties over and construct some examples.
19.
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
20.
Markus Perling 《Geometriae Dedicata》2007,127(1):121-129
We describe the construction of a class of toric varieties as spectra of homogeneous prime ideals.
相似文献