广义内射性与von Neumann正则性

引入ＩＣＥ－内射它是拟内射的推广，利用它来研究ｖｏｎ Ｎｅｕｍａｎｎ正则环、遗传环、Ａｒｔｉｎ半单环。     

由环的幂零性所确定的根

结合环中的环的幂零性不是根性质。为此，本文将结合环中的幂零理想概念扩展为次拟幂零理想和拟幂零理想，定义次拟幂零根ＳＮ和拟幂零根ＱＮ，证明它们均为Ａｍｉｔｓｕｒ－Ｋｕｒｏｓｈ根，且二者相等，进一步，我们给出了ＱＮ－半单环的构造命题和ＱＮ－根的模刻划。     

关于环的变换性条件的若干注记

关于环的变换性条件的若干注记戴跃进（福建师范大学数学系，福州３５０００７）关键词字，半素环，Ｊ－半单环，次直和。分类号ＡＭＳ（１９９１）１６Ｕ８０／ＣＣＬＯ１５３．３本文运用下列熟知的引理证明了某些环的变换性定理并推广了Ｈ．Ｅ．Ｂｅｌｌ￣［４］中若干...     

幂等元生成的正则Г—半群

本文考虑了（Ｅ（Ｓ））－由正则Г－半群Ｓ的幂等元生成的子Г－半群，着重研究了〈Ｅ（Ｓ）〉和Ｓ之间的关系，讨论了〈Ｅ（Ｓ）〉＝Ｓ的情形。     

快速并行乘幂法及反幂法

快速并行乘幂法及反幂法李磊（西安交通大学数学系，青森大学信息系统工程系）ＡＦＡＳＴＰＡＲＡＬＬＥＬＡＬＧＯＲＩＴＨＭＦＯＲＴＨＥＰＯＷＥＲＭＥＴＨＯＤＡＮＤＴＨＥＩＮＶＥＲＳＥＰＯＷＥＲＭＥＴＨＯＤ￥ＬｉＬｅｉ（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｘｉ＇ａｎＪ...     

有幺单Γ－环类所确定的上根

结合环根论中由具有单位元的单环类所确定的上根就是Ｂｒｏｗｎ－ＭｃＣｏｙ根．本文指出在Γ－环中，鉴于Γ－环单位元的复杂性质使得有幺单Γ－环类确定的上根演变成８个，进而研究了这些根之间及这些根与Γ－环其它根之间的大小关系．     

具有正规中间幂等元的富足半群的构造

本文研究富足半群上中间幂等元的若干性质，并给出了具有正规中间幂等元的富半群的构造。作为推论，我们得到Ｂｌｙｔｈ和ＭｃＦａｄｄｅｎ［１］及Ｅ１－Ｑａｌｌａｌｉ［２］中相应结果。     

Equicontinuous Seton Locally Convex Spaces

Ｌｅｔ（Ｅ，γ）ｂｅａｌｏｃａｌｌｙｃｏｎｖｅｘｓｐａｃｅａｎｄＥ′ｉｔｓｃｏｎｊｕｇａｔｅｓｐａｃｅ．ＡＥ′ｂｅａｎｅｑｕｉｃｏｎｔｉｎｕ－ｏｕｓｓｅｔｏｎ（Ｅ，γ）．ＴｈｅｗｅｌｌｋｎｏｗｎＡｌａｏｇｌｕ－ＢｏｕｒｂａｋｉＴｈｅｏｒｅｍ（［１］Ｐ２４８）ｓｔａｔｅｓｔｈａｔｅａｃｈｅ－ｑｕｉｃｏｎｔｉｎｕｏｕｓｓｅｔｏｎ（Ｅ，γ）ｉｓσ（Ｅ′，Ｅ）ｒｅｌａｔｉｖｅｌｙｃｏｍｐａｃｔｓｕｂｓｅｔ．Ｎｅｖｅｒｔｈｅｌｅｓｓ，ｅｑｕｉｃｏｎｔｉｎｕｏｕｓｓｅｔｉｓσ（Ｅ′，Ｅ）ｒｅｌａｔｉｖｅｌ…     

关于Lovasz不等式的几类超图

本文证明了下面的定理：若超图Ｈ＝（Ｘ；Ｅ１，Ｅ２，．．．Ｅｍ）中存在浓度为Ｋ长为ｍ的圈，则有ｍ∑ｉ＝１（│Ｅｉ│－ｋ）＞ｎ－ｋ。     

A STABILITY THEOREM FOR A CERTAIN FOURH-ORDER VECTOR DIFFERENTIAL FQUATION

ＡＳＴＡＢＩＬＩＴＹＴＨＥＯＲＥＭＦＯＲＡＣＥＲＴＡＩＮＦＯＵＲＨ－ＯＲＤＥＲＶＥＣＴＯＲＤＩＦＦＥＲＥＮＴＩＡＬＦＱＵＡＴＩＯＮ￥Ａ．Ｍ．Ａ．Ａｂｏｕ－Ｅｌ－Ｅｌａ＆Ａ．Ｉ．Ｓａｄｅｋ（ＦａｃｕｌｔｙｏｆＳｃｉｅｎｃｅ，ＡｓｓｉｕｔＵｎｉｖｅｒｓｉ...     

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     

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.     

Strong Cleanness of Matrix Rings Over Commutative Rings

Let R be a commutative local ring. It is proved that R is Henselian if and only if each R-algebra which is a direct limit of module finite R-algebras is strongly clean. So, the matrix ring 𝕄 _n (R) is strongly clean for each integer n > 0 if R is Henselian and we show that the converse holds if either the residue class field of R is algebraically closed or R is an integrally closed domain or R is a valuation ring. It is also shown that each R-algebra which is locally a direct limit of module-finite algebras, is strongly clean if R is a π-regular commutative ring.     

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．     

本原分式 Artin 的 Exchange 环上矩阵环

文章证明了：如果Ｒ或要为本原Ａｒｔｉｎ的Ｅｘｃｈａｎｇｅ环,则Ｍｎ（Ｒ）≌（Ｓ）当且仅当Ｒ≌Ｓ。     

Polynomial Rings Over Symmetric Rings Need Not be Symmetric

Let R be a ring with identity. The polynomial ring over R is denoted by R[x] with x its indeterminate. It is shown that polynomial rings over symmetric rings need not be symmetric by an example.     

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.     

Polynomial Rings over Symmetric Rings Need Not Be Symmetric

Let R be a ring with identity. The polynomial ring over R is denoted by R[x] with x its indeterminate. It is shown that polynomial rings over symmetric rings need not be symmetric by an example.     

强symmetric环

为了统一交换环和约化环的层表示,Lambek引进了Symmetric环.继续symmetric环的研究,定义引入了强symmetric环的概念,研究它的一些扩张性质.证明环R是强symmetric环当且仅当R[x]是强symmetric环当且仅当R[x;x~(-1)]是强symmetric环.也证明对于右Ore环R的经典右商环Q,R是强symmetric环当且仅当Q是强symmetric环.