共查询到20条相似文献,搜索用时 93 毫秒
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本文在模糊命题演算的形式演绎系统L~*中引入了封闭理论的概念,讨论了封闭理论的基本性质,并利用封闭理论给出了形式演绎系统L~*的基于公式集的完备性的证明.首先,在形式演绎系统L~*中引入了封闭理论的概念,给出了理论封闭化扩张的方法;其次,在形式演绎系统L~*中引入了完全封闭理论的概念,证明了满足相关条件的完全封闭理论的存在性;第三,对形式演绎系统L~*中的封闭理论确定的同余关系性质进行了讨论,在公式集中引入了强同余关系的概念,给出了封闭理论和强同余关系相互决定的方法;第四,在形式演绎系统L~*中证明了封闭理论型L~*-Lindenbaum代数是R_0代数,并且封闭理论型L~*-Lindenbaum代数是全序的当且仅当封闭理论是完全的;最后,利用完全封闭理论型L~*-Lindenbaum代数完成了形式系统L~*完备性的证明,并改进了原有的结果. 相似文献
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设E是特征零的代数封闭域,LE是E上L型有限维单李代效,F是E的包含素子域Q的子域,且|E:F]<∞.本文引入李代数的准子代数的概念,且F上同类型李代数LF就是LE的准子代数.本文定出了LE的包含LF的所有准子代数. 相似文献
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设■是复Hilbert空间,■是■上有界线性算子全体,■是标准算子代数且对于伴随运算封闭.本文结合广义Jensen等式证明了标准算子代数■上的和导子有关的函数方程具有广义Hyers-Ulam-Rassias稳定性. 相似文献
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Cartan型模李超代数W的二阶上同调群H2(W,F) 总被引:1,自引:1,他引:0
本文研究了有限维广义Witt李超代数W的二阶上同调群H2(W,F),其中F是一个特征P>2的代数封闭域.通过计算W到W*的导子,得到H2(W,F)是平凡的.应用此结果,我们可得W的中心扩张是平凡的. 相似文献
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姚裕丰 《数学年刊A辑(中文版)》2012,33(4):483-496
设L=H(2r;1)或K(2r+1;1)是定义在特征p>2的代数封闭域F上的限制Hamiltonian型或Contact型李代数.在对广义Jacobson-Witt代数及特殊代数不可约表示的研究基础上,通过定义L的如下阶化:L=L[q],I,其中I是{1,2,…,r}的子集,得到当p-特征函数χ是正则半单时,所有不可约Uχ(L)-模都是从不可约Uχ(L[O].I)-模诱导的. 相似文献
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<正> 五、Stone的拓广先介绍几个基本概念。定义设A是定义在点集E上的实函数族,如果对于任何f,g∈A和任意实数α,β,有αf+βg∈A且f·g∈A,即A对于加法、乘法和数乘是封闭的,则称A是E上的一个(函数)代数。例如所有多项式全体(在实轴或任一区间上)成一多项式代数。E上的连续函数全体记 相似文献
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D. E. Voloshyn 《Ukrainian Mathematical Journal》2011,63(7):1013-1022
The structure of nodal algebras over a complete discrete valuation ring with algebraically closed residue field is described. 相似文献
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N. A. Koreshkov 《Russian Mathematics (Iz VUZ)》2010,54(9):30-35
In this paper, we describe finite-dimensional homogeneously simple algebras of associative type whose 1-component is a full
matrix algebra. In addition, we prove that a finite-dimensional division ring of associative type over an algebraically closed
field is isomorphic to a group algebra. 相似文献
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Ignacio Ojeda 《代数通讯》2013,41(10):3722-3735
In this article, we prove that every binomial ideal in a polynomial ring over an algebraically closed field of characteristic zero admits a canonical primary decomposition into binomial ideals. Moreover, we prove that this special decomposition is obtained from a cellular decomposition which is also defined in a canonical way and does not depend on the field. 相似文献
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Given an affine domain of GelfandKirillov dimension 2over an algebraically closed field, it is shown that the centralizerof any non-scalar element of this domain is a commutative domainof GelfandKirillov dimension 1 whenever the domain isnot polynomial identity. It is shown that the maximal subfieldsof the quotient division ring of a finitely graded Goldie algebraof GelfandKirillov dimension 2 over a field F all havetranscendence degree 1 over F. Finally, centralizers of elementsin a finitely graded Goldie domain of GelfandKirillovdimension 2 over an algebraically closed field are considered.In this case, it is shown that the centralizer of a non-scalarelement is an affine commutative domain of GelfandKirillovdimension 1. 2000 Mathematics Subject Classification 16P90. 相似文献
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Takanori Nagamine 《代数通讯》2018,46(10):4265-4272
In this paper, we study some properties of coordinates in the polynomial ring by introducing some concepts which are weaker than coordinates. In particular, in the polynomial ring in two variables over an algebraically closed field of characteristic zero, we show some relations between polynomials and their fibers on 𝔸2. 相似文献
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[1 ]给出复数域C上多元多项式环 C[x1 ,x2 ,… ,xn]的一类整除性定理 ,本文把它推广为任意代数闭域 k上多元多项式环 k[x1 ,x2 ,… ,xn]的情形 . 相似文献
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We survey the construction of the Cox ring of an algebraic variety X and study the birational geometry of X when its Cox ring is finitely generated.
Basic notation. Throughout this paper k is an algebraically closed field. 相似文献
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We prove that n pairwise commuting derivations of the polynomial ring (or the power series ring) in n variables over a field k of characteristic 0 form a commutative basis of derivations if and only if they are k-linearly independent and have no common Darboux polynomials. This result generalizes a recent result due to Petravchuk and is an analogue of a well-known fact that a set of pairwise commuting linear operators on a finite dimensional vector space over an algebraically closed field has a common eigenvector. 相似文献
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SUMIT KUMAR UPADHYAY SHIV DATT KUMAR RAJA SRIDHARAN 《Proceedings Mathematical Sciences》2013,123(4):469-478
In this article we give a bound on the number of generators of a finitely generated projective module of constant rank over a commutative Noetherian ring in terms of the rank of the module and the dimension of the ring. Under certain conditions we provide an improvement to the Forster–Swan bound in case of finitely generated projective modules of rank n over an affine algebra over a finite field or an algebraically closed field. 相似文献
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Kirby C. Smith 《代数通讯》2013,41(4):331-346
Let R be a noncommutative polynomial ring over the division ring K where K has center F. Then R = K[x,σ,D]where σ is a monomorphism of K and D is a σ-derivaton K. R is called dimension finite if (K: Fσ)<∞ and (K: FD)<∞ where Fσ is the subfield of F fixed under σand FD is the subfied of F of D-constants. R is algebraically closed if every nonconstant polynomial in Rfactors completely into linear factors. The algebraically closed dimension finite polynomial rings are determined. s done by reducing the problem to two classes: skew polynomial rings and differential polynomial rings. Examples algebraically closed polynomial rings which are not dimensfinite are given. 相似文献