On exchange rings with primitive factor rings artinian

Abstract

In this paper we introduce generalized ideal-stable regular rings. It is shown that if a regular ring R is a generalized I-stable ring, then every square matrix over I is the product of an idempotent matrix and an generalized invertible matrix and admits a diagonal reduction by some generalized invertible matrices.     

关于强Armendariz环和强拟Armendariz环

提出了强拟Armendariz环的概念,给出了强Armendariz环和强拟Armendariz环上的一些结果.     

On JB-Rings

A ring R is a QB-ring provided that aR bR=R with a,b∈R implies that there exists a y∈R such that a by∈R_q~(-1).It is said that a ring R is a JB-ring provided that R/J(R)is a QB-ring,where J(R)is the Jacobson radical of R.In this paper,various necessary and sufficient conditions,under which a ring is a JB-ring,are established.It is proved that JB-rings can be characterized by pseudo-similarity.Furthermore,the author proves that R is a JB-ring iff so is R/J(R)~2.     

A Note on Compositions of Derivations of Prime Rings

Abstract

In this note we discuss when compositions of derivations can be nonzero derivations of prime rings. In particular we answer two questions posed by Lanski.     

Bounds on the number of isolates in sum graph labeling

A simple undirected graph H is called a sum graph if there is a labeling L of the vertices of H into distinct positive integers such that any two vertices u and v of H are adjacent if and only if there is a vertex w with label L(w)=L(u)+L(v). The sum number σ(G) of a graph G=(V,E) is the least integer r such that the graph H consisting of G and r isolated vertices is a sum graph. It is clear that σ(G)|E|. In this paper, we discuss general upper and lower bounds on the sum number. In particular, we prove that, over all graphs G=(V,E) with fixed |V|3 and |E|, the average of σ(G) is at least

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. In other words, for most graphs, σ(G)Ω(|E|).     

素环上的T—导子

设R是一环,可加映射d称为T－导子,如果对于任意a,b∈R,有d(ab)=T(a)d(b) d(a)T(b),其中T是R的非恒等自同态,本引入素环上T－导子的概念,研究其性质,并得出两个主要结果。     

Cyclic Maximal Ideals of Rings of Differential Operators over Power Series Rings

For an integral domain R, several necessary and sufficient conditions are given for R to be unibranched inside its absolute integral closure; one such condition is that R^pbe Henselian for each prime ideal P of R. Additional conditions are given in case R is a going-down domain. Unlike the situation in the Noetherian context, such going‐down domains R need not be quasilocal or of Krull dimension at most 1. A number of examples are given for the locally pseudo‐valuation domain case     

Ideal-comparability over Regular Rings

We introduce the concept of ideal-comparability condition for regular rings. Let I be an ideal of a regular ring R. If R satisfies the I-comparability condition, then R is one-sided unit-regular if and only if so is R/I. Also, we show that a regular ring R satisfies the general comparability if and only if the following hold： （1） R/I satisfies the general comparability; （2） R satisfies the general I-comparability condition; （3） The natural map B（R） → B（R/I） is surjective.     

Subdirect Products of Preadditive Categories and Weak Equivalences

We study the notions of coproduct and subdirect product of preadditive categories and prove a Birkhoff type theorem showing that every skeletally small preadditive category is a subdirect product of subdirectly irreducible, skeletally small, preadditive categories. Moreover, we show that every direct-sum decomposition of the monoid of the isomorphism classes of objects of is weakly induced by a coproduct decomposition of the preadditive category . Partially supported by Gruppo Nazionale Strutture Algebriche e Geometriche e loro Applicazioni of Istituto Nazionale di Alta Matematica, Italy. This paper was written during a visit of the second author at the Dipartimento di Matematica Pura e Applicata (Università di Padova, Italy). He acknowledges the kind hospitality received.     

Cover-preserving embeddings of distributive lattices

In this paper we investigate the Cover-Preserving-Embedding-Property, for finite distributive lattices with respect to the variety of modular lattices and give a sufficient condition. Received September 27, 1995; accepted in final form April 6, 1998.     

Approximating call-scheduling makespan in all-optical networks

We study the problem of routing and scheduling requests of limited durations in all-optical networks with restrictions on the number of available wavelengths on each link. The task is servicing the requests, assigning each of them a route from source to destination, a starting time and a wavelength with the goal of minimizing the overall time needed to serve all requests. We study the relationship between this problem and minimum path coloring and we show how to exploit known results on path coloring to derive approximation scheduling algorithms for meshes, trees and nearly-Eulerian, uniformly high-diameter graphs. We also propose different approximation algorithms for stars, trees and in trees of rings.     

Sum choice numbers of some graphs

Let f be a function assigning list sizes to the vertices of a graph G. The sum choice number of G is the minimum ∑_v∈V(G)f(v) such that for every assignment of lists to the vertices of G, with list sizes given by f, there exists proper coloring of G from the lists. We answer a few questions raised in a paper of Berliner, Bostelmann, Brualdi, and Deaett. Namely, we determine the sum choice number of the Petersen graph, the cartesian product of paths , and the complete bipartite graph K_3,n.     

一类环的结构

设Ｒ是一结合环，Ｎ表示Ｒ的所有幂零元形成的集合．本文证明了：定理如果环Ｒ满足条件：对于任意ｘ_１…，ｘ＿ｋ∈Ｒ，存在依赖于ｘ_１，…，ｘ_k的字ω_１＝ω_１（ｘ₂，…，ｘ_k）和ω₂＝ω₂（ｘ_１，…，ｘ_k-１）满足｜ω_１｜ｘ_k＞１，｜     

Topological insights from the Chinese Rings

L. Kauffman conjectured that a particular solution of the Chinese Rings puzzle is the simplest possible. We prove his conjecture by using low-dimensional topology and group theory. We notice also a surprising connection between the Chinese Rings and Habiro moves (related to Vassiliev invariants).

     

The tame and the wild automorphisms of polynomial rings in three variables

A characterization of tame automorphisms of the algebra of polynomials in three variables over a field of characteristic is obtained. In particular, it is proved that the well-known Nagata automorphism is wild. It is also proved that the tame and the wild automorphisms of are algorithmically recognizable.

     

Rings with Zassenhaus Families of Ideals

Let R be a ring with identity. We call a family ? of left ideals of R a Zassenhaus family if the only additive endomorphisms of R that leave all members of ? invariant are the left multiplications by elements of R. Moreover, if R is torsion-free and there is some left R-module M such that R ? M ? R?_?? and End _?(M) = R we call R a “Zassenhaus ring”. It is well known that all Zassenhaus rings have Zassenhaus families. We will give examples to show that the converse does not hold even for torsion-free rings of finite rank.     

Subdirect sums of weakly chained diagonally dominant matrices

Some sufficient conditions ensuring that the subdirect sum of two weakly chained diagonally dominant matrices is in this class, are given. In particular, it is shown that the subdirect sum of overlapping principal submatrices of a weakly chained diagonally dominant matrix is also a weakly chained diagonally dominant matrix.     

半群环的幂等元

讨论了半群环R[S]的幂等元问题．对[1]提出的公开问题9作了一个肯定回答，同时就一般半群环的幂等元的具体形式作了深入的研究，给出了若干情形下的幂等元刻划．