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1.
Summary For a commutative cancellative semigroup S, we define the rank of S intrinsically. This definition implies that the rank of S equals the usual rank of its group of quotients. We also characterize the rank in terms of embeddability into a rational vector space of the greatest power cancellative image of S.  相似文献   

2.
We discuss the structure of the Weierstrass semigroup at a pair of points on an algebraic curve. It is known that the Weierstrass semigroup at a pair (P, Q) contains the unique generating subset (P, Q). We find some characterizations of the elements of (P, Q) and prove that, for any point P on a curve, (P, Q) consists of only maximal elements for all except for finitely many points QP on the given curve. Also we obtain more results concerning special and nonspecial pairs.  相似文献   

3.
In this paper, it is proved that the Boolean centre of a semigroup S with sufficiently many commuting idempotents is isomorphic to the inverse limit of the directed family of Birkhoff centres (or Boolean centres) of a class of bounded semigroups. The Birkhoff centre is defined for any poset and proved that it is a relatively complemented distributive lattice whenever it is nonempty. It is observed that for a semilattice S, the Birkhoff centres as a semigroup and as a poset coincide. Also it is observed that for a Lattice (L, , ), the Birkhoff centres of the semilattices (L, ) and (L, ) coincide with the Birkhoff centre of L. Finally it is proved that for a lattice (L, , ), the Boolean centres of the semilattices (L, ) and (L, ) coincide with the Boolean centre of L.AMS Subject classification (1991): 06A12, 20M15  相似文献   

4.
5.
We obtain a necessary condition for a cohomology class on a compact locally symmetric space S()=X (a quotient of a symmetric space X of the non-compact type by a cocompact arithmetic subgroup of isometries of X) to restrict non-trivially to a compact locally symmetric subspace S H()=Y of X. The restriction is in a 'virtual' sense, i.e. it is the restriction of possibly a translate of the cohomology class under a Hecke correspondence. As a consequence we deduce that when X and Y are the unit balls in n and m , then low degree cohomology classes on the variety S() restrict non-trivially to the subvariety S H (); this proves a conjecture of M. Harris and J-S. Li. We also deduce the non-vanishing of cup-products of cohomology classes for the variety S().  相似文献   

6.
We consider the values |q||q|q – , where is a Hurwitzian number, in other words, its continued fraction expansion includes a quasi-periodic form. Especially, we set = e 1/s , where s is a positive integer.  相似文献   

7.
In the literature (see [5, 6, 8]) there are two families of spaces called Kondratiev spaces: (c)± and (S c)± for 0 1. We investigate the relation between the spaces and show that they are topologically isomorphic when (d) L2 (d) (d) is the underlying Gel'fand triple for (c)±. In this case we also give the explicit relation between the S-transform and -transform on (c)-1 and (S c)-1, respectively.  相似文献   

8.
Rovira  Carles  Tindel  Samy 《Potential Analysis》2001,14(4):409-435
We consider the family {X , 0} of solution to the heat equation on [0,T]×[0,1] perturbed by a small space-time white noise, that is t X = X +b({X })+({X }) . Then, for a large class of Borelian subsets of the continuous functions on [0,T]×[0,1], we get an asymptotic expansion of P({X }A) as 0. This kind of expansion has been handled for several stochastic systems, ranging from Wiener integrals to diffusion processes.  相似文献   

9.
In 1986, Kowol and Mitsch studied properties of the so-called natural partial order on T(X), the total transformation semigroup defined on a set X. In particular, they determined when two total transformations are related under this order, and they described the minimal and maximal elements of (T(X), ). In this paper, we extend that work to the semigroup P(X) of all partial transformations of X, compare with another natural partial order on P(X), characterise the meet and join of these two orders, and determine the minimal and maximal elements of P(X) with respect to each order.This author gratefully acknowledges the generous support of Centro de Matematica, Universidade do Minho, Portugal during his visit in May–June 2001.Received May 27, 2002; in revised form November 27, 2002 Published online May 16, 2003  相似文献   

10.
LetE R/2Z be closed with Lebesgue measure 0. We imbed the pseudo-measuresTsupported byE into a space of distributions on a specific compact connected group. The reason for this approach is to make use of the more tractable differentiable absolutely convergent Fourier series for the general problem to determine whenT is a measure. The specific results are outlined in the Introduction. Applications of the techniques presented here are used to obtain new criteria that a Helson set be a set of spectral synthesis in the author's forthcoming work (viz., A Support Preserving Hahn-Banach Property and the Helson-S Set Problem and The Helson-S Set Problem and Discontinuous Homomorphisms on Metric Algebras).  相似文献   

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