交换环上矩阵代数的局部化导子

Let R be a commutative ring with identity, Nn（R） the matrix algebra consisting of all n × n strictly upper triangular matrices over R. Several types of proper local derivations of Nn（R） （n ≤ 4） are constructed, based on which all local derivations of Nn（R） （n ≤ 4） are characterized when R is a domain.     

可换环上一类矩阵代数的导子和自同构

决定了含幺可换环上一类矩阵代数的所有导子和所有自同构.     

The Brauer-Clifford Group for (S,H)-Azumaya Algebras over a Commutative Ring

The Brauer-Clifford group BrClif(Z,G) corresponding to a finite group G and a finite-dimensional semisimple G-algebra Z was recently introduced by Alexandre Turull in the course of his work on character correspondence conjectures in group representation theory. This Brauer-Clifford group is a group of equivalence classes of Azumaya algebras over Z whose G-algebra structure agrees on restriction to the fixed (and usually nontrivial) G-algebra structure of Z. In this paper we extend the notion of the Brauer-Clifford group to the case of (S,H)-Azumaya algebras, when H is a cocommutative Hopf algebra and S is a commutative H-module algebra. These Brauer-Clifford groups turn out to be an example of the Brauer group of the symmetric monoidal category of S # H-modules, a perspective which allows one to construct a dual Brauer-Clifford group for the category of S-modules with compatible right H-comodule structure.     

交换环上严格上三角矩阵半群的自同构(英文)

设R是任意含有单位元的交换环,N_n(R)是R上的所有n×n严格上三角矩阵组成的乘法半群.本文对N_n(R)的任意自同构给出了详细的描述.     

含幺Clifford半群上的Rees矩阵半群的同余和正规加密群结构

给出了含幺Clifford半群上的Rees矩阵半群S的正规加密群结构,证明了在含幺Clifford半群上的Rees矩阵半群S上以下两个条件是等价的:(1)S上的同余ρ是完全单半群同余;(2)S上的同余ρ和S上的相容组之间存在保序双射.最后还证明了S上的完全单半群同余所构成的同余格是半模的.     

A Connection Between the Reticulation of a Ring of Quotients and the Localization Lattice of the Reticulation of a Commutative Ring

Through this article, R denotes a commutative ring with identity. The aim of this article is to construct a morphism of lattices between the reticulation of a ring of quotients (of a commutative ring with respect to a Gabriel topology) and the localization lattice of the reticulation of the initial ring. The article is structured as follows: The first section introduces all the necessary notions required to simplify the reading of the article. The second section presents some properties of the topology induced by a Gabriel topology on the reticulation L(R). In the third section the morphism δ, which achieves the intended link, is constructed. The last section studies the defined morphism in some particular cases.     

The Circle Semigroup of a Ring

Let R be a ring and define x ○ y = x + y - xy, which yields a monoid (R, ○), called the circle semigroup of R. This paper investigates the relationship between the ring and its circle semigroup. Of particular interest are the cases where the semigroup is simple, 0-simple, cancellative, 0-cancellative, regular, inverse, or the union of groups, or where the ring is simple, regular, or a domain. The idempotents in R coincide with the idempotents in (R, ○) and play an important role in the theory developed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modules with Few Types over a Commutative Valuation Ring

It is proved that a module M over a countable commutative valuation ring has few models if and only if M is ω-stable. Let T be an arbitrary complete theory of modules over either a countable serial ring or a countable commutative Prüfer ring or a countable hereditary Noetherian prime ring. It is proved that Martin's conjecture is true for T. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 74, Algebra-15, 2000.     

交换环上一类完备李代数

In this paper, we obtain a new kind of complete Lie algebra over a commutative ring, which is the Lie algebra consisting of all n × n anti-symmetric matrices over a 2-torsionfree commutative ring with identity.     

结合环上全矩阵环的Behrens根

Szasz在[2]中建议考察结合环上全矩阵环的Behrens根,本文完全解决了这一公开问题.本文摘要曾以研究通讯形式发表在“科学通报”1987年第12期上.     

Hopf Algebra Dual to a Polynomial Algebra over a Commutative Ring

For a polynomial algebra in several variables over a commutative ring R with a Hopf algebra structure the existence of the dual Hopf algebra is proved.     

交换半环上三角矩阵代数的自同构

证明了如果尺是含有恒等元的交换半环，那么R上的n阶上三角矩阵代数的自同构都是内自同构．     

交换环上上三角矩阵的李三导子

Let T(n,R) be the Lie algebra consisting of all n × n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T(n,R)-bimodule.In this paper,we prove that every Lie triple derivation d : T(n,R) → M is the sum of a Jordan derivation and a central Lie triple derivation.     

交换环上Rao正则矩阵的广义Cramer法则

Gong Z,Aldeen M和Elsner L在[A note on a generalized Cramer’s rule,Linear AlgebraApp.,2002,340:253-254]中给出结论:对任意的k,α∈Qk,n,β∈Qk,m有|Xα,β|=|A-1|AYαβ,其中A∈n×n可逆矩阵,AX=Y.本文给出交换环上Rao正则矩阵的广义Cramer法则.     

The Compressed Annihilator Graph of a Commutative Ring

Let R be a commutative ring. In this paper, we introduce and study the compressed annihilator graph of R. The compressed annihilator graph of R is the graph AG_E(R), whose vertices are equivalence classes of zero-divisors of R and two distinct vertices [x] and [y] are adjacent if and only if ann(x)∪ann(y) ? ann(xy). For a reduced ring R, we show that compressed annihilator graph of R is identical to the compressed zero-divisor graph of R if and only if 0 is a 2-absorbing ideal of R. As a consequence, we show that an Artinian ring R is either local or reduced whenever 0 is a 2-absorbing ideal of R.     

可换环上矩阵代数的SZ-导子, PZ-导子 和 S-导子

Let R be a commutative ring with identity, Nn（R） the matrix algebra consisting of all n × n strictly upper triangular matrices over R with the usual product operation. An R-linear map φ ： Nn（R） → Nn（R） is said to be an SZ-derivation of Nn（R） if x2 = 0 implies that φ（x）x＋xφ（x） = 0. It is said to be an S-derivation of Nn（R） if φ（x2） = φ（x）x＋xφ（x） for any x ∈ Nn（R）. It is said to be a PZ-derivation of Nn（R） if xy = 0 implies that φ（x）y＋xφ（y） = 0. In this paper, by constructing several types of standard SZ-derivations of Nn（R）, we first characterize all SZ-derivations of Nn（R）. Then, as its application, we determine all S-derivations and PZ- derivations of Nn（R）, respectively.     

环上伴随矩阵的若干性质探讨

本文探讨了交换环上伴随矩阵的若干性质,给出了整环上的两个主要结论.这些均推广了域上的情形.