Completions of Convexly Ordered Valuation Rings

We prove that every convexly ordered valuation ring has a unique completion as a uniform space, which furthermore is a convexly ordered valuation ring. In addition, we give a model theoretic characterisation of complete convexly ordered valuation rings, and give a necessary and sufficient condition for the completion of a convexly ordered valuation ring to be a real closed ring. Mathematics Subject Classification : 03C60, 13L05, 54E15.     

Punctual definability on structures

We study punctual categoricity on a cone and intrinsically punctual functions and obtain complete structural characterizations in terms of model-theoretic notions. As a corollary, we answer a question of Bazhenov, Downey, Kalimullin, and Melnikov by showing that relational structures are not punctually universal. We will also apply this characterisation to derive an algebraic characterisation of relatively punctually categorical mono-unary structures.     

On the characterisation of paired monotone metrics

Hasegawa and Petz introduced the notion of paired monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the paired family. In this paper we show that the characterisation theorem holds true under hypotheses that are more general than those used in the above quoted references.     

Flat and Stably Flat Modules

We study Kropholler's generalisation of Lazard's criterion for a module to be flat. The context is complete cohomology and modules of type (FP)_∞. Let G be a group in the class ₁ of groups which act on a finite dimensional contractible cell complex with finite stabilisers and let R be a strongly G-graded algebra. We provide a characterisation of the stably flat R-modules under the assumption that R₁ is coherent of finite global dimension.     

A characterisation of the planes meeting a non-singular quadric of PG(4,Q) in a conic

By counting and geometric arguments, we provide a combinatorial characterisation of the planes meeting the non-singular quadric of PG(4,q) in a conic. A characterisation of the tangents and generators of this quadric when q is odd has been proved by de Resmini [15], and we give an alternative using our result.     

Concerning a characterisation of Buekenhout-Metz unitals

In [7], for the casesq even andq=3, a characterisation of the Buekenhout-Metz unitals inPG(2,q ²) was given. We complete this characterisation by proving the result forq>3.     

Modules Whose Endomorphism Rings are Division Rings

The well-known Schur's Lemma states that the endomorphism ring of a simple module is a division ring. But the converse is not true in general. In this paper we study modules whose endomorphism rings are division rings. We first reduce our consideration to the case of faithful modules with this property. Using the existence of such modules, we obtain results on a new notion which generalizes that of primitive rings. When R is a full or triangular matrix ring over a commutative ring, a structure theorem is proved for an R-module M such that End _R (M) is a division ring. A number of examples are given to illustrate our results and to motivate further study on this topic.     

右对称环

本文在左对称环的基础上提出了右对称环的概念,分别给出了是右对称环但不是左对称环和是左对称环但不是右对称环的例子．证明了（1）如果R是Armendariz环,则R是右对称环的充要条件R[x]是右对称环;（2）如果R是约化环,则R[x]/（x^n）是右对称环,其中（xn）是由xn生成的理想．     

J-clean环的推广

如果R中每个元素(对应地,可逆元)均可表示为一个幂等元与环R的Jacobson根中一个元素之和,则称环R是J-clean环(对应地,UJ环).所有的J-clean环都是UJ环.作为UJ环的真推广,本文引入GUJ环的概念,研究GUJ环的基本性质和应用.进一步地,研究每个元素均可表示为一个幂等元与一个方幂属于环的Jacobson根的元素之和的环.     

A new characterisation of hereditary pi rings

In this paper we prove a new characterisation of hereditary PI rings, namely we show that a Noetherian, but not Artinian, PI ringR that is an order in an Artinian ring splits into a direct sum of an Artinian ring of finite representation type and hereditary semiprime rings if and only if all its proper Artinian factor rings are of finite representation type. We also show, through examples, that the above characterisation does not hold for some more general settings. Supported by the EC via TMR-Fellowship ERB4001GT63713.     

On CS Rings and QF Rings

In this paper, we shall discuss the conditions for a right SC right CS ring to be a QF ring. In particular, we prove that if R is a right SI right CS ring satisfying the reflexive orthogonal condition (*) and if every CS right R-module is -CS, then R is a QF ring.AMS Subject Classification (1991): 16L30 16L60     

No-arbitrage with multiple-priors in discrete time

In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. We show that it is equivalent to the existence of a subclass of priors having the same polar sets as the initial class and such that the uni-prior no-arbitrage holds true for all priors in this subset. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated.     

关于SIS环

通过自内射环和半本原环给出了SIS环的定义,即如果RRR是内射的并且J(R)=0,我们称此环为SIS环;并且得到了它的一些刻画和性质.     

环的Armendariz性

研究了一个环何时具有Armendariz性．使用环论的一般方法,证明了在一定条件下商环、具有一对零同态的Morita Context环以及映射环是Armendariz环,推广了已有的某些结果．     

Ore Extensions of Skew Armendariz Rings

Let α be an endomorphism and δ an α-derivation of a ring R. We introduce the notion of skew-Armendariz rings which are a generalization of α-skew Armendariz rings and α-rigid rings and extend the classes of non reduced skew-Armendariz rings. Some properties of this generalization are established, and connections of properties of a skew-Armendariz ring R with those of the Ore extension R[x; α, δ] are investigated. As a consequence we extend and unify several known results related to Armendariz rings.     

Reflexive Property of Rings

Mason introduced the reflexive property for ideals, and then this concept was generalized by Kim and Baik, defining idempotent reflexive right ideals and rings. In this article, we characterize aspects of the reflexive and one-sided idempotent reflexive properties, showing that the concept of idempotent reflexive ring is not left-right symmetric. It is proved that a (right idempotent) reflexive ring which is not semiprime (resp., reflexive), can always be constructed from any semiprime (resp., reflexive) ring. It is also proved that the reflexive condition is Morita invariant and that the right quotient ring of a reflexive ring is reflexive. It is shown that both the polynomial ring and the power series ring over a reflexive ring are idempotent reflexive. We obtain additionally that the semiprimeness, reflexive property and one-sided idempotent reflexive property of a ring coincide for right principally quasi-Baer rings.     

Constructing ultraweakly continuous functionals on

In this paper we give a constructive characterisation of ultraweakly continuous linear functionals on the space of bounded linear operators on a separable Hilbert space.

     

α-对称环

引入α-对称环的概念,讨论了它与其它相关环的关系,证明环R是α-对称环当且仅当R上的n×n上三角矩阵环T_n(R)是α-对称环;若R是α-对称环,则R[x]/(x~n)是α-对称环,其中(x~n)是由x~n生成的理想,n为任意正整数.     

广义中心α-Armendariz环

本文引入广义中心α-Armendariz环的概念,得到了广义中心α-Armendariz环的基本性质,研究了广义中心α-Armendariz环与其他环之间的一些关系.     

Ideal-Symmetric and Semiprime Rings

Lambek extended the usual commutative ideal theory to ideals in noncommutative rings, calling an ideal A of a ring R symmetric if rst ∈ A implies rts ∈ A for r, s, t ∈ R. R is usually called symmetric if 0 is a symmetric ideal. This naturally gives rise to extending the study of symmetric ring property to the lattice of ideals. In the process, we introduce the concept of an ideal-symmetric ring. We first characterize the class of ideal-symmetric rings and show that this ideal-symmetric property is Morita invariant. We provide a method of constructing an ideal-symmetric ring (but not semiprime) from any given semiprime ring, noting that semiprime rings are ideal-symmetric. We investigate the structure of minimal ideal-symmetric rings completely, finding two kinds of basic forms of finite ideal-symmetric rings. It is also shown that the ideal-symmetric property can go up to right quotient rings in relation with regular elements. The polynomial ring R[x] over an ideal-symmetric ring R need not be ideal-symmetric, but it is shown that the factor ring R[x]/xⁿR[x] is ideal-symmetric over a semiprime ring R.