关于赵君喜“R_n~∞中一个幂等元的构造”一文的意见

本文证明了“中一个幂等元的构造”一文中的幂等元Ｑ不是套代数ａｌｇＮ中的算子，因此也不是如该文作者所断言的是中的元。     

关于分次代数的一个Fong型定理

证明有限p-可解群G的特征p的域上的分次代数的任一投射不可分模是从它的一个Hall p′-子群H的分次子代数的模的诱导模; 并且给出了它的Hall p′-子群H的分次子代数的投射不可分模的诱导模仍然不可分的充分必要条件.     

关于N（2，2，0）代数的中间幂等元

为了深入研究N（2,2,0）代数的代数结构,在N（2,2,0）代数中建立了中间幂等元的概念,讨论了它的基本性质,给出了中间幂等元关联的集合坞是（S,＊,△,0）的子代数的一个条件．证明了当U（2,2,0）代数中包含一个右零半群时,Mg是幂等元集E（S）的子集．并利用坞定义了一个等价关系．     

关于赵君喜“R^∞N中一个幂等元的构造”一文的意见

本文证明了“Ｒ＾∞Ｎ中一个幂等元的构造”一文中幂等元Ｑ不是套代数ａｌｇＮ中的算了，因此也不是如该文作者所断言的是Ｒ＾∞Ｎ中的元。     

关于循环子半群的结构与数量问题及拟环的特征与结构

彻底解决了所有循环半群及其子群的结构和数量问题,并讨论了拟群分解问题,同时,对群论基本定理作了部分推广,并给出了定理的另一部分不可推广的反例,最后,建立了一类特殊环－拟环。     

代数矩阵和算子的相似分类

运用Gelfand表示定理和Silov幂等元定理得到半单n-齐次Banach代数 的一个中心分解定理,进而利用此定理给出两个强不可约Cowen-Douglas算子的相似分类.     

关于两个特殊环曲面码的参数

扩充了Hansen的关于几个环曲面码的结果,给出两个新的环曲面码,并且用上同调的方法来计算码的维数,用相交理论的方法来估计最小距离,主要目的是为了证明对应两个不同的多边形可能具有相同的参数.最后,证明了这些新的码在某些有限域上是最好的码.     

JB代数中的面结构

本文描述了含单元元的ＪＢ代数及其对偶空间的单位球和这些单位球的正部的闭面。     

等幂和的循环积分程序

等幂和的循环积分程序王云葵（广西灌阳高级中学５４１６００）等幂和Ｓｍ（ｎ）＝１ｍ＋２ｍ＋…＋ｎｍ是一个历史悠久，肇源颇深的古老问题．早在两千多年前，希腊数学家阿基米德在其著《螺线》中就记载着前三个等幂和公式：Ｓ１（ｎ）＝１２ｎ（ｎ＋１），Ｓ２（ｎ）＝...     

胞腔代数中的Rota-Baxter代数结构（英文）

一个带有非平凡幂等元的结合代数带有自然的Rota-Baxter代数结构.本文研究胞腔代数的不同拟幂等元给出的Rota-Baxter结构间的同构关系.     

Construction of Certain Cyclic Distance-Preserving Codes Having Linear-Algebraic Characteristics

An ordered list of binary words of length n is called a distance-preserving m, n-code, if the list distance between two words is equal to their Hamming distance, for distances up to m. A technique for constructing cyclic m, n-codes is presented, based on the standard Gray code and on some simple tools from linear algebra.     

The Theory of Cyclic Codes and a Generalization to Additive Codes

We present a new approach to the theory of cyclic and constacyclic codes and generalize the theory to cover the family of additive (not necessarily linear) cyclic codes. The approach is based on the action of the Galois group (cyclotomic cosets). The conventional representation of cyclic codes as ideals in a factor ring of the polynomial ring is not needed.     

On Galois Extension of Hopf Algebras

Let H be a cosemisimple Hopf algebra over a field k, and π ： A→ H be a surjective cocentral bialgebra homomorphism of bialgebras. The authors prove that if A is Galois over its coinvariants B=LH Ker π and B is a sub-Hopf algebra of A, then A is itself a Hopf algebra. This generalizes a result of Cegarra [3] on group-graded algebras.     

Affine Invariant and Cyclic Codes over p-adic Numbers and Finite Rings

Affine invariant and cyclic codes over p-adic numbers and over integers modulo p ^d are studied. It has been determined what cyclic codes have an extension that is affine invariant.     

The Automorphism Groups of BCH Codes and of Some Affine-Invariant Codes Over Extension Fields

Affine-invariant codes are extended cyclic codes of length p ^m invariant under the affine-group acting on . This class of codes includes codes of great interest such as extended narrow-sense BCH codes. In recent papers, we classified the automorphism groups of affine-invariant codes berg, bech1. We derive here new results, especially when the alphabet field is an extension field, by expanding our previous tools. In particular we complete our results on BCH codes, giving the automorphism groups of extended narrow-sense BCH codes defined over any extension field.     

The Covering Radius of Ternary Cyclic Codes with Length up to 25

The covering radius of all ternary cyclic codes of length up to 25 is given. Some of the results were obtained by computer and for others mathematical reasonings were applied. The minimal distances of all codes were recalculated.     

Cyclic Codes Over\mathbb{Z}_{4} of Even Length

We determine the structure of cyclic codes over for arbitrary even length giving the generator polynomial for these codes. We determine the number of cyclic codes for a given length. We describe the duals of the cyclic codes, describe the form of cyclic codes that are self-dual and give the number of these codes. We end by examining specific cases of cyclic codes, giving all cyclic self-dual codes of length less than or equal to 14. San Ling - The research of the second named author is partially supported by research Grants MOE-ARF R-146-000-029-112 and DSTA R-394-000-011-422.     

On Hopf Galois Extension of Separable Algebras

In this paper, the classical Galois theory to the H*-Galois case is developed. Let H be a semisimple and cosemisimple Hopf algebra over a field k, A a left H-module algebra,and A/AHa right H*-Galois extension. The authors prove that, if AHis a separable kalgebra, then for any right coideal subalgebra B of H, the B-invariants A~B= {a ∈ A |b · a = ε(b)a, b∈ B} is a separable k-algebra. They also establish a Galois connection between right coideal subalgebras of H and separable subalgebras of A containing AHas in the classical case. The results are applied to the case H =(kG)*for a finite group G to get a Galois 1-1 correspondence.