Lattices of interpretability types of varieties

Let be the set of all primes, the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as , and , where AD is a variety of -divisible Abelian groups with unique taking of the pth root _p(x) for every p , is a variety of -modules over a normal field , contained in , and G_n is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that , and are distributive lattices, with and where ub and ub_f are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005.     

Global construction of associated orders in complex multiplication

Let E/L be an elliptic curve defined over a number field L with complex multiplication by the ring of integers of a quadratic imaginary number field K⊆L. We fix a prime ideal p in K and assume E to have good reduction modulo p. We consider cosets of the form P+G_m, where G_m denotes the group of points of order p^m and P a point of order p^r+m, , which can be viewed as the set of all “p^m-th roots” of some point in G_r.In analogy to the Kummer theory such a coset gives rise to the definition of an order in an algebra M_P and to an associated order A defined below by its local components. These objects naturally come into play in the Galois module structure of rings of integers in ray class fields over K. It is the aim of this article to construct global generators both for and A as algebras over the ring of integers of L. For the convenience of the reader we also include from (J. Number Theory 77 (1999) 97) a simple construction of Galois generators for over A. We thereby show that these generators also fit in the setting of this article that is more general than in [Sch4]. The main results in Theorems 3, 6 and 7 are obtained assuming the base field L to contain “enough” torsion points of E.     

Dual Entwining Structures and Dual Entwined Modules

In this note we introduce and investigate the concepts of dual entwining structures and dual entwined modules. This generalizes the concepts of dual Doi–Koppinen structures and dual Doi–Koppinen modules introduced (in the infinite case over rings) by the author in his dissertation. Presented by A. VerschorenMathematics Subject Classifications (2000) 16W30, 18E15.Jawad Y. Abuhlail: Current address: Department of Mathematical Sciences, P.O. Box 5046, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Saudi Arabia.     

Characterization of Morita Equivalence Pairs of Quantales

We characterize the pairs of sup-lattices which occur as pairs of Morita equivalence bimodules between quantales in terms of the mutual relation between the sup-lattices.     

Estimating a skein module with characters

We introduce a new technique for estimating the number of generators of the Kauffman bracket skein module of a three manifold; one which requires the construction of linear functionals on a simpler version of the module. Of particular interest is the use of representations of the fundamental group into to generate the functionals.

     

Characterization of eventually periodic modules in the singularity categories

The singularity category of a ring makes only the modules of finite projective dimension vanish among the modules, so that the singularity category is expected to characterize a homological property of modules of infinite projective dimension. In this paper, among such modules, we deal with eventually periodic modules over a left artin ring, and, as our main result, we characterize them in terms of morphisms in the singularity category. As applications, we first prove that, for the class of finite dimensional algebras over a field, being eventually periodic is preserved under singular equivalence of Morita type with level. Moreover, we determine which finite dimensional connected Nakayama algebras are eventually periodic when the ground field is algebraically closed.     

A simplified presentation of Specht modules

Fulton and Kraskiewicz gave a presentation of Specht modules as a quotient of the space of column tabloids by dual Garnir relations. We simplify this presentation by showing that it can be generated by a single relation for each pair of columns of a tableau with ordered columns, thereby significantly reducing the number of generators given in the original construction. Our presentation applies to all Specht modules, and is of a similar nature to a recent result by Friedmann-Hanlon-Stanley-Wachs that applies to staircase partitions. We show that our presentation implies the Friedmann-Hanlon-Stanley-Wachs presentation.     

Gleeble-3800热模拟试验机故障的检测及处理

介绍了Gleeble-3800热模拟试验机运行一年来陆续出现的一些故障及对故障的排查过程和解决方法.     

关于Kellogg定理的若干推广

本文以连续模,光滑模为工具,讨论由单位圆至光滑的若当曲线Ｌ所范单连通区的保角映射问题,对于Ｋｅｌｌｏｇｇ定理作了较大幅度的推广,得出了新的结果。     

Structure indices for multidimensional systems

The structure indices of a one-dimensional system are an importantset of invariants. In this paper we examine a generalizationof this concept to multidimensional linear systems, which correspondsto the algebraic concept of a Hilbert series. We use the standardtheory of the Hilbert series to explain some of the previousID system-theoretic results. We discuss the computation of nDstructure indices from an initial condition set, and the invariantswhich can be derived from these indices.