共查询到20条相似文献,搜索用时 93 毫秒
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本文研究了两个代数张量积的Grothendieck群K0首先构作三个群同态Ψ1,ΨⅡ,ΨⅢ,并证明:若R为增广Δ0代数,则存在K0(R)k0(A)K0(S)的子群C使得K0,并存在K0(R)K1(S)的子群D使得K1(S)。然后给出在群代数和包络代数方面的应用,最后考虑K0(R)≌Z的增广代数的情形。 相似文献
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DR0代数:由De Morgan代数导出的正则剩余格 总被引:3,自引:0,他引:3
首先讨论了De Morgan代数与剩余格的关系,并引入强De Morgan代数的概念,讨论了它的基本性质.随后,将著名的R0蕴涵拓广到De Morgan代数上,称为广义R0蕴涵;证明了添加广义凰蕴涵和相应 算子后的De Morgan代数L成为剩余格的充要条件是L为强De Morgan代数,并由此引入D‰代数的概念.接着,研究了DR0代数与‰代数的关系,证明了以下结论:Boole代数是DR0代数;全序DR0代数和全序R0代数等价;DR0代数是R0代数当且仅当它满足预线性条件;无中点的DR0代数是BL代数当且仅当它是Boole代数.最后,举例说明了非D兄D代数的RD代数、以及非R0代数的DR0代数都是存在的. 相似文献
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HEYTING代数与FUZZY蕴涵代数 总被引:5,自引:0,他引:5
Heyting代数是作为直觉主义命题逻辑的代数模型而引进的Fuzzy蕴涵代数是 [0 ,1]值逻辑的蕴函联结词的一种代数抽象 .本文给出Heyting代数的若干基本性质 ,并证明了Heyting代数是Fuzzy蕴涵代数 ,也是Heyting型Fuzzy蕴涵代数。 相似文献
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Heyting代数是作为直觉主义命题逻辑的代数模型而引起的,Fuzzy蕴涵代数是[0,1]值逻辑的蕴涵联结词的一种代数抽象。本文给出Heyting代数的若干基本性质,并证明了Heyting代数是Fuzzy蕴涵代数,也是Heyting型Fuzzy蕴涵代数。 相似文献
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引入了BCK-代数的范数与距离的概念,给出了赋范BCK-代数的一些基本性质,证明了赋范BCK-代数的同构(同态)像和原像仍是赋范BCK-代数,研究了BCK-代数与BCK-代数笛卡儿之间的赋范性质关系.并且引入了赋范BCK-代数的点列极限概念,研究了极限的相关性质.讨论了有界赋范BCK-代数的与模糊BCK-代数的关系. 相似文献
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《模糊系统与数学》2014,(2)
伪BCK-代数是非可换模糊逻辑(蕴涵片段)的基本代数框架,伪BCI-代数是伪BCK-代数的推广,本文研究伪BCI-代数的结构。首先,借助BZ-代数(又称弱BCC-代数)给出伪BCI-代数的一个特征性质;其次,通过引入群逆伪BCI-代数的概念,研究了伪BCI-代数与(非可换)群之间的关系;接着,引入群逆滤子、优滤子和正规滤子的概念,并通过它们给出伪BCI-代数成为群逆伪BCI-代数(以及滤子成为p-滤子)的充要条件;最后,证明了如下结论:(1)平均伪BCI-代数等价于p-半单BCI-代数;(2)伪BCI-代数的每一个滤子是p-滤子,当且仅当它是群逆的且其伴随群的每一个子群是正规子群。 相似文献
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MTL代数的特征定理 总被引:3,自引:1,他引:2
对于逻辑系统代数结构的研究,是一个十分重要的研究课题.近期提出的BL代数,R_0代数,MTL代数就是这个方向具有代表性的研究成果.本文讨论MTL代数的性质与结构,给出这种代数的几个特征定理,澄清这种代数与其它代数结构的关系.鉴于单位区间中由左连续t-范数诱导的剩余蕴涵与MTL代数的紧密联系,本文还考察了这种模糊蕴涵的特征性质. 相似文献
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In this note we supply an elementary proof of the following well-known theorem of R. Stanley: the -vectors of Gorenstein algebras of codimension 3 are SI-sequences, i.e. are symmetric and the first difference of their first half is an -sequence.
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Guoxing Ji Tomoyoshi Ohwada Kichi-Suke Saito 《Proceedings of the American Mathematical Society》2006,134(10):2975-2982
We prove that algebraic commutants of maximal subdiagonal algebras and of analytic operator algebras determined by flows in a -finite von Neumann algebra are self-adjoint.
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关于格上蕴涵代数及其对偶代数 总被引:2,自引:0,他引:2
给出了格蕴涵代数、MV代数、R0代数等一些格上蕴涵代数之间的关系,并建立了它们的对偶代数.其结果描述了这些代数内部结构的特征,同时也为从语义的角度进一步研究格值逻辑系统提供了一个新的途径. 相似文献
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The aim of this paper is to investigate the first Hochschild
cohomology of admissible algebras which can be regarded as a
generalization of basic algebras. For this purpose, the authors
study differential operators on an admissible algebra. Firstly,
differential operators from a path algebra to its quotient algebra
as an admissible algebra are discussed. Based on this discussion,
the first cohomology with admissible algebras as coefficient modules
is characterized, including their dimension formula. Besides, for
planar quivers, the $k$-linear bases of the first cohomology of
acyclic complete monomial algebras and acyclic truncated quiver
algebras are constructed over the field $k$ of characteristic $0$. 相似文献
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A Poisson algebra is a Lie algebra endowed with a commutative associative product in such a way that the Lie and associative products are compatible via a Leibniz rule. If we part from a Lie color algebra, instead of a Lie algebra, a graded-commutative associative product and a graded-version Leibniz rule we get a so-called Poisson color algebra (of degree zero). This concept can be extended to any degree, so as to obtain the class of Poisson color algebras of arbitrary degree. This class turns out to be a wide class of algebras containing the ones of Lie color algebras (and so Lie superalgebras and Lie algebras), Poisson algebras, graded Poisson algebras, z-Poisson algebras, Gerstenhaber algebras, and Schouten algebras among other classes of algebras. The present paper is devoted to the study of structure of Poisson color algebras of degree g0, where g0 is some element of the grading group G such that g0 = 0 or 4g0≠0, and with restrictions neither on the dimension nor the base field, by stating a second Wedderburn-type theorem for this class of algebras. 相似文献
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This paper provides a method for the computation of Yoneda algebras for algebras of dihedral type. The Yoneda algebras for
one infinite family of algebras of dihedral type (the family in K. Erdmann’s notation) are computed. The minimal projective resolutions of simple modules were calculated by an original
computer program implemented by one of the authors in C++ language. The algorithm of the program is based on a diagrammatic
method presented in this paper and inspired by that of D. Benson and J. Carlson.
This work was partially supported by the grant 06-01-00200 of the Russian Foundation for Basic Research. 相似文献
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作为拟三角弱Hopf代数的推广,我们引入了半拟三角弱Hopf代数的概念.令(H,R,v)是一个半拟三角弱Hopf代数,其中,R是其半拟三角结构.我们指明R保持了拟三角弱Hopf代数中泛R-矩阵的许多基本性质.特别地,讨论了Drinfeld元的性质,证明其是可逆的并且是余作用v的余不变量.另外,证明了半拟三角弱Hopf代数的对极平方是对合的. 相似文献
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David P. Blecher Masayoshi Kaneda 《Proceedings of the American Mathematical Society》2004,132(7):2103-2113
A left ideal of any -algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Conversely, we show here that operator algebras with a r.c.a.i. should be studied in terms of a certain left ideal of a -algebra. We study operator algebras and their multiplier algebras from the perspective of ``Hamana theory' and using the multiplier algebras introduced by the first author.