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1.
Isao Kikumasa Kiyoichi Oshiro Hiroshi Yoshimura 《Applied Categorical Structures》2008,16(1-2):297-310
We study to classify, up to isomorphism, algebras Λ over a field k such that the radical cubed is zero and Λ modulo the radical is a product of copies of k. The number of local quasi-Frobenius k-algebras with the condition is shown to be not less than the cardinality of k. In particular, the canonical forms of those algebras of dimension 5 are presented and their isomorphism classes are completely
determined under some conditions on k.
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Sergey V. Tikhonov 《代数通讯》2013,41(11):4735-4744
Let k be a field, K/k be a quadratic separable field extension, and 𝒜 a finite dimensional central simple algebra over K. If k is global or the field of fractions of a two-dimensional excellent henselian local domain with an algebraically closed residue field of characteristic zero and the degree of 𝒜 is odd, we prove that all K/k-involutions on 𝒜 are cyclic. 相似文献
4.
Robert Wisbauer 《Applied Categorical Structures》2008,16(1-2):255-295
Algebras and coalgebras are fundamental notions for large parts of mathematics. The basic constructions from universal algebra
are now expressed in the language of categories and thus are accessible to classical algebraists and topologists as well as
to logicians and computer scientists. Some of them have developed specialised parts of the theory and often reinvented constructions
already known in a neighbouring area. One purpose of this survey is to show the connection between results from different
fields and to trace a number of them back to some fundamental papers in category theory from the early 1970s. Another intention
is to look at the interplay between algebraic and coalgebraic notions. Hopf algebras are one of the most interesting objects
in this setting. While knowledge of algebras and coalgebras are folklore in general category theory, the notion of Hopf algebras
is usually only considered for monoidal categories. In the course of the text we do suggest how to overcome this defect by
defining a Hopf monad on an arbitrary category as a monad and comonad satisfying some compatibility conditions and inducing an equivalence between
the base category and the category of the associated bimodules. For a set G, the endofunctor G× – on the category of sets shares these properties if and only if G admits a group structure. Finally, we report about the possibility of subsuming algebras and coalgebras in the notion of
(
F
,
G
)-dimodules associated to two functors between different categories. This observation, due to Tatsuya Hagino, was an outcome from the theory of categorical data
types and may also be of use in classical algebra.
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5.
Emil Jeřábek 《Archive for Mathematical Logic》2007,46(2):73-92
We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic
logics. We state a broad condition under which the admissibility problem is coNEXP-hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC) is in coNE, thus obtaining a sharp complexity estimate for admissibility in these systems.
The research was done while the author was visiting the Department of Philosophy of the Utrecht University. Supported by grant
IAA1019401 of GA AV ČR 相似文献
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A new approach for admissibility analysis of the direct discontinuous Galerkin method through Hilbert matrices
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Chad N Vidden 《Numerical Methods for Partial Differential Equations》2016,32(1):350-367
This article continues the study of the so‐called direct discontinuous Galerkin (DDG) method for diffusion problems as developed in [Liu and Yan, SIAM J Numer Anal 47 (2009), 475–698;, Liu and Yan, Commun Comput Phys 8 (2010), 541–564; C. Vidden and J. Yan, J Comput Math 31 (2013), 638–662; H. Liu, Math Comp (in press)]. A key feature of the DDG method lies with the numerical flux design which includes two (or more) free parameters. This article identifies the class of all admissible numerical flux choices (Theorem 2.2) for degree n polynomial approximations for the symmetric DDG method [C. Vidden and J. Yan, J Comput Math 31 (2013), 638–662], guaranteeing stability of the resulting method. Our main contribution is the new technique of analysis for the DDG admissibility condition. The strategy is to directly evaluate the admissibility condition (Lemma 2.4) by choosing a simple polynomial basis. The admissibility condition is then transformed into an eigenvalue problem resulting in showing needed properties of inverse Hilbert matrices (Lemma 2.3, Appendix). Numerical tests are provided to confirm theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 350–367, 2016 相似文献
8.
Luis Alberto Wills-Toro 《代数通讯》2013,41(12):5019-5049
We study not necessarily associative (NNA) division algebras over the reals. We classify in this paper series those that admit a grading over a finite group G, and have a basis {v g |g ∈ G} as a real vector space, and the product of these basis elements respects the grading and includes a scalar structure constant with values only in {1, ? 1}. We classify here those graded by an abelian group G of order |G| ≤8 with G non–isomorphic to ?/8?. We will find the complex, quaternion, and octonion algebras, but also a remarkable set of novel non–associative division algebras. 相似文献
9.
Luís Felipe Gonçalves Fonseca 《代数通讯》2018,46(4):1630-1640
Let F be an infinite field and let Mn(F) be the algebra of n×n matrices over F endowed with an elementary grading whose neutral component coincides with the main diagonal. In this paper, we find a basis for the graded polynomial identities of Mn(F) with the transpose involution. Our results generalize for infinite fields of arbitrary characteristic previous results in the literature, which were obtained for the field of complex numbers and for a particular class of elementary G-gradings. 相似文献
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Yasumasa Saisho 《Probability Theory and Related Fields》1987,74(3):455-477
Summary In this paper we prove that there exists a unique solution of the Skorohod equation for a domain inR
d
with a reflecting boundary condition. We remove the admissibility condition of the domain which is assumed in the work [4] of Lions and Sznitman. We first consider a deterministic case and then discuss a stochastic case. 相似文献
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It is well-known that only a single condition (called the admissibility condition) is sufficient for L 2-convergence of multiple continuous wavelet transforms (MCWT). However known results suggest that to guarantee the pointwise convergence of MCWT for L p -functions wavelets should vanish quite rapidly at infinity. In this article, we consider the class of nonseparable multiple wavelets with square-symmetric Fourier transforms. For these wavelets ψ we prove that the admissibility condition and the condition ψ∈L 1(R n ) are sufficient for the convergence of corresponding MCWT almost everywhere. 相似文献
14.
《代数通讯》2013,41(4):1765-1775
Abstract This paper studies two homogenizations of the down-up algebras introduced in Benkart and Roby (Benkart, G., Roby, T. (1998). Down-up Algebras. J. Algebra 209:305–344). We show that in all cases the homogenizing variable is not a zero-divisor, and that when the parameter β is non-zero, the homogenized down-up algebra is a Noetherian domain and a maximal order, and also Artin-Schelter regular, Auslander regular, and Cohen-Macaulay. We show that all homogenized down-up algebras have global dimension 4 and Gelfand-Kirillov dimension 4, and with one exception all homogenized down-up algebras are prime rings. We also exhibit a basis for homogenized down-up algebras and provide a necessary condition for a Noetherian homogenized down-up algebra to be a Hopf algebra. 相似文献
15.
《Quaestiones Mathematicae》2013,36(5):623-629
AbstractWe present a new admissibility theorem for Galois structures in the sense of G. Janelidze. It applies to relative exact categories satisfying a suitable relative modularity condition, and extends the known admissibility theorem in the theory of generalized central extensions. We also show that our relative modularity condition holds in every relative exact Goursat category. 相似文献
16.
In this article, we give a sufficient condition for a Lie color algebra to be complete. The color derivation algebra Der(?) and the holomorph L of finite dimensional Heisenberg Lie color algebra ? graded by a torsion-free abelian group over an algebraically closed field of characteristic zero are determined. We prove that Der(?) and Der(L) are simple complete Lie color algebras, but L is not a complete Lie color algebra. 相似文献
17.
This paper presents a construction of the n = 2 (mod 4) Clifford algebra Cl
n,0-valued admissible wavelet transform using the admissible similitude group SIM(n), a subgroup of the affine group of
\mathbbRn{\mathbb{R}^{n}} . We express the admissibility condition in terms of the Cl
n,0 Clifford Fourier transform (CFT). We show that its fundamental properties such as inner product, norm relation, and inversion
formula can be established whenever the Clifford admissible wavelet satisfies a particular admissibility condition. As an
application we derive a Heisenberg type uncertainty principle for the Clifford algebra Cl
n,0-valued admissible wavelet transform. Finally, we provide some basic examples of these extended wavelets such as Clifford
Morlet wavelets and Clifford Hermite wavelets. 相似文献
18.
Bangteng Xu 《代数通讯》2013,41(5):1279-1297
ABSTRACT A commutative algebra with the identity (a * b) * (c * d) ? (a * d) * (c * b) = (a, b, c) * d ? (a, d, c) * b is called Novikov–Jordan. Example: K[x] under multiplication a * b = ?(ab) is Novikov–Jordan. A special identity for Novikov–Jordan algebras of degree 5 is constructed. Free Novikov–Jordan algebras with q generators are exceptional for any q ≥ 1. 相似文献
19.
We give a generalization of the Stone–Weierstrass property for subalgebras of C (X), with X a completely regular Hausdorff space. In particular, we study in this paper some subalgebras of C0(X), with X a locally compact Hausdorff space, provided with weighted norm topology. By using the Stone–Weierstrass property, we then describe the ideal structure of these algebras. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
《代数通讯》2013,41(4):1837-1858
Abstract We present “canonical forms” of finite dimensional (quasi-Frobenius) commutative algebras Λ over a field k such that the radical cubed is zero and Λ modulo the radical is a product of copies of k. We also determine the isomorphism classes of the algebras Λ over some typical fields. 相似文献