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1.
研究了拟正则半环上的同余,给出了拟正则半环上一类理想的性质,并利用这类理想给出了拟正则半环上可除半环同余的几种等价形式.  相似文献   

2.
环并半环称为纯整环并半环, 若其加法幂等元集是一个带半环. 若纯整环并半环的加法幂等元集是一个T带半环, 称为$T$纯整环并半环. 研究了纯整环并半环以及一些$T$纯整环并半环的半群结构.  相似文献   

3.
引入可除半环的伪理想,它与同余互相唯一决定,在可除半环中利用理想作商是可行的,并证明了同态基本定理.  相似文献   

4.
满足a+ab=a+b幂等半环的结构   总被引:1,自引:0,他引:1  
本讨论了满足a ab=a b的幂等半环的结构,给出了这种幂等半环是左零半环的伪强右正规幂等半环,并得出这种幂等半环与环的直积是左环的伪强右正规幂等半环。  相似文献   

5.
环并半环   总被引:6,自引:0,他引:6       下载免费PDF全文
称环的无交并组成的半环为环并半环. 环并半环的全体形成一个簇B, 它包含了环和幂等元半环. 特别地, 它包含了分配格簇. 给出了环并半环的若干结构定理, 进一步, 借此揭示了B的子簇格的结构.  相似文献   

6.
给定一个集合Ω,引入了可补半环的Ω-模糊可补子半环的概念,研究了它的一些基本性质。给出了可补半环的Ω-模糊可补子半环的等价刻画,证明了可补半环的Ω-模糊可补子半环的交、同态像与同态原像等也是可补半环的Ω-模糊可补子半环。最后,通过在SΩ上定义运算+,×,-,得到可补半环(SΩ,+,×,-),并研究了与其相关的模糊可补子半环与Ω-模糊可补子半环。  相似文献   

7.
研究了完全正则半环的特征.利用半群的方法,得到了当分配半环的乘法幂等元集分别是左零带、矩形带以及正规带时,该类半环成为完全正则半环的等价刻画,推广并改进了相关文献的主要结果.  相似文献   

8.
在半环中引入了一类理想的概念,讨论了这类理想的性质,并研究了一类广义正则半环上的同余,给出了这类半环上一种半环同余的特征.  相似文献   

9.
半环半直积的同构定理   总被引:1,自引:0,他引:1  
半群半直积及封闭性刻划于文[1],为将半直积的研究推广至半环中,本文首先在交换半环与交换半群的直积上定义加法及乘法运算,从而构造了一类半环;半环半直积.并讨论了半环半直积的同构等问题.  相似文献   

10.
加法可换可消半环的一个结构定理及应用   总被引:1,自引:0,他引:1  
郑玉美  游松发 《数学进展》1993,22(4):358-361
半环是一种有很好实际背景和应用前景的代数结构,尤其对于计算机语言的研究有极为重要的作用。因此,对半环的研究越来越引起人们的关注。本文首先证明了每个加法可换可消半环有一个包环,然后在此基础上证明了它们是多重线性等价的,最后证明了加法可消的交换半坏上的Levitzki-Amitsur定理。  相似文献   

11.
Let B be a closed dissipative operator in a Hilbert space ? with an arbitrary domain of definition. We investigate briefly the problem of describing all the closed (and, in particular, the closed maximal) dissipative extensions B of the operator B. Following this we introduce the concept of a generalized resolvent of a closed dissipative operator with an arbitrary domain of definition, and we study the fundamental properties of generalized resolvents.  相似文献   

12.
We consider closed biharmonic hypersurfaces in a Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic hypersurfaces in space forms. As an application of this formula, we reobtain a result concerning the closed biharmonic hypersurfaces in Euclidean spheres that lie in a closed hemisphere.  相似文献   

13.
Motivated by the subsmoothness of a closed set introduced by Aussel et al. (2005) [8], we introduce and study the uniform subsmoothness of a collection of infinitely many closed subsets in a Banach space. Under the uniform subsmoothness assumption, we provide an interesting subdifferential formula on distance functions and consider uniform metric regularity for a kind of multifunctions frequently appearing in optimization and variational analysis. Different from the existing works, without the restriction of convexity, we consider several fundamental notions in optimization such as the linear regularity, CHIP, strong CHIP and property (G) for a collection of infinitely many closed sets. We establish relationships among these fundamental notions for an arbitrary collection of uniformly subsmooth closed sets. In particular, we extend duality characterizations of the linear regularity for a collection of closed convex sets to the nonconvex setting.  相似文献   

14.
15.
In this paper, we consider closed surfaces which contain spatial graphs. In the case that a closed surface is a 2-sphere, we show that the 2-sphere can be isotoped so that it intersects a bridge sphere for the spatial graph in a single loop. In the case that a closed surface is not a 2-sphere, we define an invariant of a spatial graph by counting the number of intersection of a compressing disk for the closed surface and the spatial graph. By using this invariant, we give a lower bound for the bridge number of a spatial graph.  相似文献   

16.
Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. ésik and W. Kuich showed that a locally closed commutative semiring is an iteration semiring (is also a Conway semiring). By study of polynomial semirings and matrix semirings, we obtain new expressions of certain polynomials and show that all matrix semirings over a locally closed semiring are also locally closed, and so a locally closed semiring (which need not be commutative) is an iteration semiring.  相似文献   

17.
Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. ésik and W. Kuich showed that a locally closed commutative semiring is an iteration semiring (is also a Conway semiring). By study of polynomial semirings and matrix semirings, we obtain new expressions of certain polynomials and show that all matrix semirings over a locally closed semiring are also locally closed, and so a locally closed semiring (which need not be commutative) is an iteration semiring.  相似文献   

18.
In generalising a closed graph theorem of Dektjarev [5] we show that each almost closed and uniformly almost continuous relation of a quasi-uniform space to a hypercomplete quasi-uniform space is uniformly continuous. The hypothesis of being almost closed is necessary and actually weaker than the requirement that the relation considered has a closed graph. Since each topological space can be quasi-uniformized, one obtains closed graph theorems for topological spaces.As consequences we get an analogous closed graph theorem for locally uniformly almost continuous relations and a theorem concerning the completeness of the range of each continuous uniformly almost open mapping of a hypercomplete space to a uniform space.Finally we prove a closed graph theorem for relations to locally compact spaces without referring to any quasi-uniformization and thus without assumptions and statements concerning uniformity.  相似文献   

19.
The KKT conditions in an optimization problem with interval-valued objective function are derived in this paper. Two solution concepts of this optimization problem are proposed by considering two partial orderings on the set of all closed intervals. In order to consider the differentiation of an interval-valued function, we invoke the Hausdorff metric to define the distance between two closed intervals and the Hukuhara difference to define the difference of two closed intervals. Under these settings, we derive the KKT optimality conditions.  相似文献   

20.
HBa(D)空间的内插定理   总被引:2,自引:0,他引:2  
研究了一类由H^p空间构成的Ba空间的内插性质,给出了H^Ba(D)空间的三个内插定理。  相似文献   

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