素环的李结构

设R是一个咎征非2的素环,U是R的一个平方封闭的李理想,d1,d2,d是R的导子,δ是R的广义导子．本文证明了U为中心李理想,如果以下条件之一成立：（1）d（x）od（y）=xoy;（2）d（x）οd（y）＋xοy=0;（3）d1（x）οd2（可）=0;（4）δ（[x,y]）=0;（5）δ（xοy）=0对所有的x,y∈U．     

On the Prime Ideal Structure of Bhargava Rings

Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be 𝔹 _x (D): = {f ∈ K[X] | ? a ∈ D, f(xX + a) ∈ D[X]}, where x ∈ D. A Bhargava ring over D is a subring of the ring of integer-valued polynomials over D. In this article, we study the prime ideal structure and calculate the Krull and valuative dimension of Bhargava rings over a general domain D.     

On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings

The ring decomposition technique of part I is extended to the case when the factors in the direct product decomposition are no longer fields but arbitrary chain rings. This includes not only the case of quasi-cyclic codes over rings but also the case of quasi-cyclic codes over fields whose co-index is no longer prime to the characteristic of the field. A new quaternary construction of the Leech lattice is derived.     

K-本原环的结构

研究K-本原环.证明了素环R是K-本原环当且仅当R含有一个非零理想I是K-本原环,当且仅当eRe是K-本原环,其中e是R的非零幂等元.并证明了GPI素环是K-本原环.推广了文献中的相应结果.     

一般环之分式环

本文给出一般环R之分式环△^-1R的构造和△^-R的理想的一些性质,推广了现有中外教科书的结论．证明了（1）△^-1R中理想有且仅有形式△^-1I,其中△3R．（2）如果P是R的素理想,且△∩P=Ф,则△^-1P是△^-1R的素理想,且θ^-1（△^-1P）=P。     

On Quotient Rings in Alternative Rings

We introduce a notion of left nonsingularity for alternative rings and prove that an alternative ring is left nonsingular if and only if every essential left ideal is dense, if and only if its maximal left quotient ring is von Neumann regular (a Johnson-like Theorem). Finally, we obtain a Gabriel-like Theorem for alternative rings.     

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     

分次单环的结构

A characterization of gr-simple rings is given by using the notion of componentwise-dense subrings of a full matrix ring over a division ring. As a consequence, any G-graded full matrix ring over a division ring is isomorphic to a dense subring of a full matrix ring with a good G-grading. Some conditions for a grading of a full matrix ring to be isomorphic to a good one are given, which generalize some results in: Dascascu, S., Lon, B., Nastasescu, C. and Montes, J. R., Group gradings on full matrix rings, J. Algebra, 220(1999), 709-728.     

On Valuation Rings

In this article, we provide necessary and sufficient conditions for R = A ∝ E to be a valuation ring where E is a non-torsion or finitely generated A-module. Also, we investigate the (n, d) property of the valuation ring.     

On Hopfian Rings

The main results proved in this paper are:(i) If R is a boolean hopfian ring then the polynomial ring R[T] is hopfian.(ii) Let R and S be hopfian rings. Suppose the only central idempotents in S are 0 and 1 and that S is not a homomorphic image of R. Then R × S is a hopfian ring.     

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.     

On d-Free Rings

Abstract

The recent development of the theory of functional identities is based on the concept of d-freeness introduced by Beidar and Chebotar. This concept involves two conditions, the first one concerns the situation when the expression ∑ _i E _i x _i  + ∑ _j x _j F _j is always zero, and the second one the situation when this expression is always central. We discuss the relationship between these two conditions and in particular we establish that in general they are independent of each other.     

On Köthe Rings

Mathematische Annalen -     

子半理想环

本文提出了环论中的一个新概念：子半理想，得到了群环为子半理想环的一个充要条件。     

On the Representation of Finite Rings by Matrices over Commutative Rings

In this paper, it is shown that all finite associative rings satisfying the identities nx?=?0 and x ³ f(x)?+?x ²?=?0, where n is an odd natural number and f(x) ∈ ?[x], are embeddable in the ring of matrices over some suitable commutative ring.     

On the Formation of Vortex Rings

The production of a vortex ring formed by using a piston to drive fluid through an orifice is considered. A cylindrical vortex sheet is supposed to be formed initially which rolls up into a vortex ring. Energy and momentum are conserved during rollup and determine the speed and size of the ring. It is shown that these quantities are independent of the vorticity distribution in the core of the ring. Reasonable agreement with experimental observations is found. A speculation is made about the criterion for the rings to be laminar or turbulent.     

The Comparable Structure of Exchange Rings

We obtain a new substitution for modules over exchange rings satisfying related comparability. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class of exchange rings satisfying related comparability. Received June 1, 1998, Revised November 15, 1999, Accepted June 1, 2000     

The Structure of Finite c-Local Rings

For a commutative ring R, assume that c is a nonzero element of Z(R) with the property that cZ(R) = {0}. A local ring R is called c-local if Z(R)² = {0, c}, Z(R)³ = {0}, and xZ(R) = {0} implies x ∈ {0, c}. For any finite c-local ring (R, 𝔪), it is proved that the ideal m has a minimal generating set which has a c-partition. The structure and classification up to isomorphism of all finite commutative c-local rings with order greater than 2⁵ are determined.