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1.
An algebra A has finite degree if its term functions are determined by some finite set of finitary relations on A. We study this concept for finite algebras in general and for finite semigroups in particular. For example, we show that
every finite nilpotent semigroup has finite degree (more generally, every finite algebra with bounded p
n
-sequence), and every finite commutative semigroup has finite degree. We give an example of a five-element unary semigroup
that has infinite degree. We also give examples to show that finite degree is not preserved in general under taking subalgebras,
homomorphic images, direct products or subdirect factors. 相似文献
2.
Julia M. N. Brown 《Designs, Codes and Cryptography》2007,44(1-3):239-248
We give a nearfield-free definition of some finite and infinite incidence systems by means of half-points and half-lines and
show that they are projective planes. We determine a planar ternary ring for these planes and use it to determine the full
collineation group and to demonstrate some embeddings of these planes among themselves. We show that these planes include
all finite regular Hughes planes and many infinite ones. We also show that PG(3, q) embeds in Hu(q
4) (and show infinite versions of this embedding).
Dan Hughes 80th Birthday. 相似文献
3.
Dessislava H. Kochloukova 《代数通讯》2013,41(3):785-796
We define and study the property finite presentability in the category of Hopf algebras that are smash product of universal enveloping algebra of a Lie algebra by a group algebra. We show that for such Hopf algebras finite presentability is equivalent with finite presentability as an associative k-algebra. 相似文献
4.
Ursula Whitcher 《代数通讯》2013,41(4):1427-1440
We consider the symplectic action of a finite group G on a K3 surface X. The Picard group of X has a primitive sublattice determined by G. We show how to compute the rank and discriminant of this sublattice. We then investigate the classification of symplectic actions by a fixed finite group, using moduli spaces of K3 surfaces with symplectic G-action. 相似文献
5.
On Minimal Realization Over a Finite Chain Ring 总被引:1,自引:0,他引:1
Graham Norton 《Designs, Codes and Cryptography》1999,16(2):161-178
Let R be a finite chain ring, e.g. a Galois ring. We give a compact recursive formula for a minimal realization of a finite R-sequence. In particular, we show how to obtain a monic minimal polynomial and a rational approximation of a finite R-sequence. We also show how to solve the classical key equation of Algebraic Coding Theory over R. 相似文献
6.
Z. Reichstein 《Commentarii Mathematici Helvetici》2003,78(1):185-202
Let k be a field and G be a finite subgroup of . We show that the ring of multiplicative invariants has a finite SAGBI basis if and only if G is generated by reflections.
Received: March 5, 2002 相似文献
7.
We introduce μ-convexity, a new kind of game convexity defined on a σ-algebra of a nonatomic finite measure space. We show that μ-convex games are μ-average monotone. Moreover, we show that μ-average monotone games are totally balanced and their core contains a nonatomic finite signed measure. We apply the results
to the problem of partitioning a measurable space among a finite number of individuals. For this problem, we extend some results
known for the case of individuals’ preferences that are representable by nonatomic probability measures to the more general
case of nonadditive representations. 相似文献
8.
Weimin Han 《Mathematical Methods in the Applied Sciences》1994,17(7):487-508
The paper is devoted to a posteriori quantitative analysis for errors caused by linearization of non-linear elliptic boundary value problems and their finite element realizations. We employ duality theory in convex analysis to derive computable bounds on the difference between the solution of a non-linear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on differences between finite element solutions of the nonlinear problem and finite element solutions of the linearized problem, by using finite element solutions of the linearized problem only. Numerical experiments show that our a posteriori error bounds are efficient. 相似文献
9.
Caroline Series 《Israel Journal of Mathematics》1979,34(3):245-258
We define a class of equivalence relations with polynomial growth and show that such relations always support finite invariant
measures and are hyperfinite. In particular, foliations of polynomial growth define hyperfinite equivalence relations with
respect to any family of finite invariant measures on transversals. We also extend a result of Dye for countable groups to
show that if a locally compact second countable groupG acts freely on a Lebesgue spaceX with finite invariant measure, so that the orbit relation onX is hyperfinite, thenG is amenable. 相似文献
10.
Using elementary counting methods, we calculate a universal perturbative invariant (also known as the LMO invariant) of a 3-manifold M, satisfying , in terms of the Alexander polynomial of M. We show that +1 surgery on a knot in the 3-sphere induces an injective map from finite type invariants of integral homology
3-spheres to finite type invariants of knots. We also show that weight systems of degree 2m on knots, obtained by applying finite type 3m invariants of integral homology 3-spheres, lie in the algebra of Alexander-Conway weight systems, thus answering the questions
raised in [Ga].
Received: 27 April 1998 / in final form: 8 August 1999 相似文献
11.
Juhani Pitkäranta 《Numerische Mathematik》1992,61(1):523-542
Summary We analyse the problem of membrane locking in (h, p) finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution. We show that in the standard finite element method, locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder. A general strategy of avoiding locking by using modified bilinear forms is introduced, and a special implementation of this strategy on aligned rectangular grids is considered. 相似文献
12.
Abstract We study the generation of a finite group by its conjugacy classes, while generalizing basic concepts from linear algebra: basis and dimension. Besides the well known Burnside Basis Theorem for finite p-groups, there is no direct extension of these concepts to other families of finite groups. We show that by considering generating sets consisting of conjugacy classes, there is a possibility for such a generalization. 相似文献
13.
Summary We study embeddings between torsion-free nilpotent groups having isomorphic localizations. Firstly, we show that for finitely
generated torsion-free nilpotent groups of nilpotency class 2, the property of having isomorphicP-localizations (whereP denotes any set of primes) is equivalent to the existence of mutual embeddings of finite index not divisible by any prime
inP. We then focus on a certain family Γ of nilpotent groups whose Mislin genera can be identified with quotient sets of ideal
class groups in quadratic fields. We show that the multiplication of equivalence classes of groups in Γ induced by the ideal
class group structure can be described by means of certain pull-back diagrams reflecting the existence of enough embeddings
between members of each Mislin genus. In this sense, the family Γ resembles the family N0 of infinite, finitely generated nilpotent groups with finite commutator subgroup. We also show that, in further analogy with
N0, two groups in Γ with isomorphic localizations at every prime have isomorphic localizations at every finite set of primes.
We supply counterexamples showing that this is not true in general, neither for finitely generated torsion-free nilpotent
groups of class 2 nor for torsion-free abelian groups of finite rank.
Supported by DGICYT grant PB94-0725
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
14.
Let K be a field complete with respect to a real valuation v and not algebraically closed. We will show that every finite codimension subfield of K is closed in the v-adic topology if and only if the degree of imperfection of K is finite. It follows that there are incomplete finite codimension subfields of K when the degree of imperfection of K is infinite. These examples exhibit other interesting pathologies. We are able to give a necessary (and in the case of a discrete real valuation also sufficient) condition for a given finite codimension subfield to be complete. Finally, we give some applications to fields of Laurent series. Communicated by A. Prestel. 相似文献
15.
The subject of this paper is to study the problem of the minimum distance to the complement of a convex set. Nirenberg has stated a duality theorem treating the minimum norm problem for a convex set. We state a duality result which presents some analogy with the Nirenberg theorem, and we apply this result to polyhedral convex sets. First, we assume that the polyhedral set is expressed as the intersection of some finite collection of m given half-spaces. We show that a global solution is determined by solving m convex programs. If the polyhedral set is expressed as the convex hull of a given finite set of extreme points, we show that a global minimum for a polyhedral norm is obtained by solving a finite number of linear programs. 相似文献
16.
We show that, if the subgroup growth of a finitely generated (abstract or profinite) groupG is super-exponential, then every finite group occurs as a quotient of a finite index subgroup ofG. The proof involves techniques from finite permutation groups, and depends on the Classification of Finite Simple Groups.The first author was partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T7441. The second author was partially supported by the Israeli National Science Foundation. 相似文献
17.
G. Peruginelli 《代数通讯》2018,46(11):4724-4738
We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring. 相似文献
18.
Let Mod(S) be the extended mapping class group of a surface S. For S the twice-punctured torus, we show that there exists an isomorphism of finite index subgroups of Mod(S) which is not the restriction of any inner automorphism. For S a torus with at least three punctures, we show that every injection of a finite index subgroup of Mod(S) into Mod(S) is the restriction of an inner automorphism of Mod(S); this completes a program begun by Irmak. We also establish the co-Hopf property for finite index subgroups of Mod(S).Dan Margalit: Partially supported by an NSF postdoctoral fellowship 相似文献
19.
Smooth Groups 总被引:3,自引:0,他引:3
Roland Schmidt 《Geometriae Dedicata》2001,84(1-3):183-206
A group is called smooth if it has a finite maximal chain of subgroups in which any two intervals of the same length are isomorphic (as lattices). We show that every finite smooth group G is a semidirect product of a p-group by a cyclic group; in particular, G is soluble. We determine the exact structure of G if G is not a p-group. 相似文献
20.
We show that the rational Novikov conjecture for a group Γ of finite homological type follows from the mod 2 acyclicity of the Higson compactification of an EΓ. We then show that for groups of finite asymptotic dimension, the Higson compactification is mod p acyclic for all p and deduce the integral Novikov conjecture for these groups. © 2007 Wiley Periodicals, Inc. 相似文献