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1.
A congruence lattice L of an algebra A is called power-hereditary if every 0-1 sublattice of Ln is the congruence lattice of an algebra on An for all positive integers n. Let A and B be finite algebras. We prove
•  If ConA is distributive, then every subdirect product of ConA and ConB is a congruence lattice on A × B.
•  If ConA is distributive and ConB is power-hereditary, then (ConA) × (ConB) is powerhereditary.
•  If ConA ≅ N5 and ConB is modular, then every subdirect product of ConA and ConB is a congruence lattice.
•  Every congruence lattice representation of N5 is power-hereditary.
Received November 11, 2004; accepted in final form November 23, 2004.  相似文献   

2.
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field % MathType!End!2!1! we contruct a % MathType!End!2!1! which
–  • is finitely generated and infinite-dimensional, but has only finitedimensional quotients;
–  • has a subalgebra of finite codimension, isomorphic toM 2(k);
–  • is prime;
–  • has quadratic growth, and therefore Gelfand-Kirillov dimension 2;
–  • is recursively presented;
–  • satisfies no identity;
–  • contains a transcendental, invertible element;
–  • is semiprimitive if % MathType!End!2!1! has characteristic ≠2;
–  • is graded if % MathType!End!2!1! has characteristic 2;
–  • is primitive if % MathType!End!2!1! is a non-algebraic extension of % MathType!End!2!1!;
–  • is graded nil and Jacobson radical if % MathType!End!2!1! is an algebraic extension of % MathType!End!2!1!.
The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted.  相似文献   

3.
We present a new pivot-based algorithm which can be used with minor modification for the enumeration of the facets of the convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary dimension. The algorithm has the following properties:
(a)  Virtually no additional storage is required beyond the input data.
(b)  The output list produced is free of duplicates.
(c)  The algorithm is extremely simple, requires no data structures, and handles all degenerate cases.
(d)  The running time is output sensitive for nondegenerate inputs.
(e)  The algorithm is easy to parallelize efficiently.
For example, the algorithm finds thev vertices of a polyhedron inR d defined by a nondegenerate system ofn inequalities (or, dually, thev facets of the convex hull ofn points inR d, where each facet contains exactlyd given points) in timeO(ndv) andO(nd) space. Thev vertices in a simple arrangement ofn hyperplanes inR d can be found inO(n 2 dv) time andO(nd) space complexity. The algorithm is based on inverting finite pivot algorithms for linear programming.  相似文献   

4.
We consider smooth non-degenerate surfaces in ℙ4, and prove that there is a finite number of such surfaces which are:
(a)  sectionally non-special, i.e.h1(O C(1))=0, where C is a general hyperplane section of S; or
(b)  not of general type and non-special (i.e. h1(O C(1))=0.
A complete list is given in both cases.  相似文献   

5.
In this article, we prove different results concerning the regularity of the C 0-Lagrangian invariant graphs of the Tonelli flows. For example :
•  in dimension 2 and in the autonomous generic case, we prove that such a graph is in fact C 1 on some set with (Lebesgue) full measure;
•  under certain dynamical additional hypothesis, we prove that these graphs are C 1.
Résumé.  Dans cet article, on démontre différents résultats concernant la régularité des graphes C 0-lagrangiens invariants par des flots de Tonelli. Par exemple :
•  en dimension 2, dans le cas autonome et générique, on montre que ces graphes sont de classe C 1 sur un ensemble de mesure (de Lebesque) pleine;
•  sous certaines hypothèses concernant la dynamique restreinte, on montre que ces graphes sont de classe C 1.
Submitted: July 23, 2007. Accepted: February 14, 2008.  相似文献   

6.
In this paper, we discuss the representation-finite selfinjective artin algebras of classB n andC n and obtain the following main results: For any fieldk, let Λ be a representation-finite selfinjective artin algebras of classB n orC n overk.
(a)  We give the configuration ofZB n andZC n.
(b)  We show that Λ is standard.
(c)  Under the condition ofk being a perfect field, we describe Λ by boundenk-species and show that Λ is a finite covering of the trivial extension of some tilted algebra of typeB n orC n.
  相似文献   

7.
We show that if (K,L) is a semi-abelian category, there exists an abelian categoryK x with the followings properties:
1  The categoryK is a full subcategory ofK x.
2  The free objects ofK are projectives inK x.
3  A sequence ofK-morphismes isK-exact if, and only if, it isK x-exact.
4  To each objectU ofK x we can associate a surjections:X→U whereX is an object ofK.
  相似文献   

8.
Let H 1, H 2 be Hilbert spaces and T be a closed linear operator defined on a dense subspace D(T) in H 1 and taking values in H 2. In this article we prove the following results:
(i)  Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T*T) of T*T, In addition, if H 1 = H 2 and T is self-adjoint, then
(ii)  inf {‖T x‖: x ∈ D(T) ∩ N(T)⊥‖x‖ = 1} = inf {|λ|: 0 ≠ λ ∈ σ(T)}
(iii)  Every isolated spectral value of T is an eigenvalue of T
(iv)  Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T) of T
(v)  σ(T) bounded implies T is bounded.
We prove all the above results without using the spectral theorem. Also, we give examples to illustrate all the above results.  相似文献   

9.
The main purpose of the paper is to strengthen previous author’s results. Let k be a field of characteristic ≠ 2, n ≥ 2. Suppose that elements are linearly independent over ℤ/2ℤ. We construct a field extension K/k and a quaternion algebra D = (u, v) over K such that
(1)  the field K has no proper extension of odd degree
(2)  the u-invariant of K equals 4
(3)  the multiquadratic extension is not 4-excellent, and the quadratic form 〈uv,-u,-v, a〉 provides a relevant counterexample
(4)  the central division algebra A = D ⊗E (a, t0) ⊗E (b1, t1) ⋯ ⊗E (bn, tn) does not decompose into a tensor product of two nontrivial central simple algebras over E, where E = K ((t0))((t1)) … ((tn)) is the Laurent series field in the variables t0, t1, …, tn
(5)  ind A = 2n+1.
In particular, the algebra A provides an example of an indecomposable algebra of index 2n+1 over a field, the u-invariant and the 2-cohomological dimension of which equal 2n+3 and n + 3, respectively. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 338, 2006, pp. 227–241.  相似文献   

10.
It is known that the unit sphere, centered at the origin in ℝ n , has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds on the complexity of the coordinates: for every point ν on the unit sphere in ℝ n , and every ν > 0; there is a point r = (r 1; r 2;…;r n) such that:
–  ⊎ ‖r-v‖∞ < ε.
–  ⊎ r is also a point on the unit sphere; Σ r i 2 = 1.
–  ⊎ r has rational coordinates; for some integers a i , b i .
–  ⊎ for all .
One consequence of this result is a relatively simple and quantitative proof of the fact that the rational orthogonal group O(n;ℚ) is dense in O(n;ℝ) with the topology induced by Frobenius’ matrix norm. Unitary matrices in U(n;ℂ) can likewise be approximated by matrices in U(n;ℚ(i))   相似文献   

11.
Abstract  This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here is a language with a distinguished linear order <, and REF consists of formulas of the form
where φ is an -formula, φ <x is the -formula obtained by restricting all the quantifiers of φ to the initial segment determined by x, and x is a variable that does not appear in φ. Our results include: Theorem    The following five conditions are equivalent for a complete first order theory T in a countable language with a distinguished linear order:
(1)  Some model of T has an elementary end extension with a first new element.
(2)  T ⊢ REF .
(3)  T has an ω 1-like model that continuously embeds ω 1.
(4)  For some regular uncountable cardinal κ, T has a κ-like model that continuously embeds a stationary subset of κ.
(5)  For some regular uncountable cardinal κ, T has a κ-like model that has an elementary extension in which the supremum of M exists.
Moreover, if κ is a regular cardinal satisfying κ = κ <κ , then each of the above conditions is equivalent to:
(6)  T has a κ + -like model that continuously embeds a stationary subset of κ.
  相似文献   

12.
M. K. Sen 《Semigroup Forum》1992,44(1):149-156
A pair (S, P) of a regular semigroupsS and a subsetP ofE s whereE s is the set of all idempotent elements ofS is called aP-regular semigroupS(P) if it satisfies the following:
(1)  P 2 ⊆E S
(2)  qPq⊆P for allq∈P
(3)  for anyx∈S there existsx †∈V(x) (the set of inverses ofx), such thatxP 1 x †⊆P andx † P 1 x⊆P whereP 1=P∩{1}.
The class of orthodox semigroups and the class of regular *-semigroups are within the class ofP-regular semigroups. This paper gives a characterisation of theP-kernel of aP-congruence.  相似文献   

13.
In this paper, we prove that for a sublinear expectation ɛ[·] defined on L 2(Ω,), the following statements are equivalent:
(i)  ɛ is a minimal member of the set of all sublinear expectations defined on L 2(Ω,)
(ii)  ɛ is linear
(iii)  the two-dimensional Jensen’s inequality for ɛ holds.
Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation. This work was supported by National Basic Research Program of China (973 Program) (Grant No. 2007CB814901) (Financial Risk) and National Natural Science Foundation of China (Grant No. 10671111)  相似文献   

14.
Let G be the automorphism group of an extension of algebraically closed fields of characteristic zero of transcendence degree n, 1 ≤ n ≤ ∞. In this paper we
•  construct some maximal closed non-open subgroups Gv, and some (all, in the case of countable transcendence degree) maximal open proper subgroups of G;
•  describe, in the case of countable transcendence degree, the automorphism subgroups over the intermediate subfields (a question of Krull, [K2, §4, question 3b)]);
•  construct, in the case n = ∞, a fully faithful subfunctor ( − )v of the forgetful functor from the category of smooth representations of G to the category of smooth representations of Gv;
•  construct, using the functors ( − )v, a subfunctor Γ of the identity functor on , coincident (via the forgetful functor) with the functor Γ on the category of admissible semilinear representations of G constructed in [R3] in the case n = ∞ and .
The study of open subgroups is motivated by the study of (the stabilizers of) smooth representations undertaken in [R1, R3]. The functor Γ is an analogue of the global sections functor on the category of sheaves on a smooth proper algebraic variety. Another result is that ‘interesting’ semilinear representations are ‘globally generated’.   相似文献   

15.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by X α,p . We show
(i)  The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented.
(ii)  The identity operator from X α,p to X α,p when p > q is unbounded.
(iii)  Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then
(iv)  duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0.
(v)  We investigate the properties of the operators from X α,p spaces to their predual.
  相似文献   

16.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
(1)  If (G, τ) has the A(iii)-property, then its completion is an order-complete locally solid lattice group.
(2)  If G is order-complete and τ has the Fatou property, then the order intervals of G are τ-complete.
(3)  If (G, τ) has the Fatou property, then G is order-dense in Ĝ and has the Fatou property.
(4)  The order-bound topology on any commutative lattice group is the finest locally solid topology on it.
As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid topological groups is established.  相似文献   

17.
LetG be a finite nonsolvable group andH a proper subgroup ofG. In this paper we determine the structure ofG ifG satisfies one of the following conditions:
(1)  Every solvable subgroupK(K⊉H) is eitherp-decomposable or a Schmidt group,p being the smallest odd prime factor of |G|.
(2)  |G∶H| is divisible by an odd prime and every solvable subgroupK(K⊉H) is either 2′-closed or a Schmidt group.
(3)  |G∶H| is even and every solvable subgroupK(K⊉H) is either 2-closed or a Schmidt group.
  相似文献   

18.
We have generalized the theory of Shannon's games in [10]. In this paper, we treat a game on a graph with an action of elementary abelian group but our decision of the winner is more general. Our theory can be applied for non-negative integersn andr, to the two games on a graph withn + 1 distinguished terminals whose rules are as follows:
(1)  the players Short and Cut play alternately to choose an edge,
(2)  the former contracts it and the later deletes it
(3)  the former if and only if he connects the terminals into at mostn – r + 1 ones.
Dedicated to Professor Sin Hitotumatu for his 60'th birthday  相似文献   

19.
An Engel condition with generalized derivations on multilinear polynomials   总被引：1，自引：1，他引：0  
Let R be a prime ring with extended centroid C, g a nonzero generalized derivation of R, f (x 1,..., x n) a multilinear polynomial over C, I a nonzero right ideal of R. If [g(f(r 1,..., r n)), f(r 1,..., r n)] = 0, for all r 1, ..., r n ∈ I, then either g(x) = ax, with (a − γ)I = 0 and a suitable γ ∈ C or there exists an idempotent element e ∈ soc(RC) such that IC = eRC and one of the following holds:
(i)  f(x 1,..., x n) is central valued in eRCe
(ii)  g(x) = cx + xb, where (c+b+α)e = 0, for α ∈ C, and f (x 1,..., x n)2 is central valued in eRCe
(iii)  char(R) = 2 and s 4(x 1, x 2, x 3, x 4) is an identity for eRCe.
Supported by a grant from M.I.U.R.  相似文献   

20.
Two partial ordersP andQ on a setX arecomplementary (written asPQ) if they share no ordered pairs (except for loops) but the transitive closure of the union is all possible ordered pairs. For each positive integern we form a graph Pos n consisting of all nonempty partial orders on {1, ,n} with edges denoting complementation. We investigate here properties of the graphs Pos n . In particular, we show:
–  The diameter of Pos n is 5 for alln>2 (and hence Pos n is connected for alln);
–  With probability 1, the distance between two members of Pos n is 2;
–  The graphs Pos n are universal (i.e. every graph occurs as an induced subgraph of some Pos n );
–  The maximal size (n) of an independent set of Pos n satisfies the asymptotic formula
  相似文献   

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