关于左完全幺半群

设Ｓ是左完全幺半群．本文讨论了左，右Ｓ－系的链条件，特别地证明了右Ｓ－系的Ｂｊｏｒｋ定理．     

图的不可收缩性和end-正则性

图的半群理论是图的群理论的延伸．图的不可收缩性和end－正则性是其中受到普遍关注的课题．本文揭示了两者之间的内在联系．     

Monoids with Stable Torsion-Free Polygons

We deal with monoids possessing a stable class of torsion-free polygons over them.     

弱拉回平坦序S-系对序幺半群的刻画

设S是序幺半群,借助环模理论以及半群S-系理论方法,在序S-系范畴中研究了弱拉回平坦性质。刻画了弱拉回平坦序S-系关于直积封闭的序幺半群类以及弱拉回平坦性质与其他性质一致的序幺半群类,讨论了循环序S-系具有拉回平坦覆盖的条件,进而推广了S-系的一些重要结果。     

for commutative rings with identity

Let , , , , be the usual operators on classes of rings: and for isomorphic and homomorphic images of rings and , , respectively for subrings, direct, and subdirect products of rings. If is a class of commutative rings with identity (and in general of any kind of algebraic structures), then the class is known to be the variety generated by the class . Although the class is in general a proper subclass of the class for many familiar varieties . Our goal is to give an example of a class of commutative rings with identity such that . As a consequence we will describe the structure of two partially ordered monoids of operators.

     

两类整环在w-算子下的刻画

通过对SM整环中准素w-理想与w-互素理想的讨论,证明了R是Krull整环当且仅当R是SM整环,w-dim(R)=1,且每个p-准素w-理想是素理想p的幂的w-包络.同时,运用w-算子,辅以t-,v-算子给出了π-整环的一些新的等价刻画.     

Enumeration of symplectic and orthogonal injective partial transformations

In this paper, we compute the generating function of , where a is a real number with a≥1. We then use this function to determine the generating functions of the symplectic and orthogonal Renner monoids. Furthermore, we show that these functions are closely related to Laguerre polynomials.     

AF-Domains and Their Generalizations

In this article, we are concerned with the study of the dimension theory of tensor products of algebras over a field k. We introduce and investigate the notion of generalized AF-domain (GAF-domain for short) and prove that any k-algebra A such that the polynomial ring in one variable A[X] is an AF-domain is in fact a GAF-domain, in particular any AF-domain is a GAF-domain. Moreover, we compute the Krull dimension of A? _k B for any k-algebra A such that A[X] is an AF-domain and any k-algebra B generalizing the main theorem of Wadsworth in [16 Wadsworth , A. R. ( 1979 ). The Krull dimension of tensor products of commutative algebras over a field . J. London Math. Soc. 19 : 391 – 401 .[Crossref], [Web of Science ®] , [Google Scholar]].     

Some Comments on the Jacobson Conjecture

Noetherian rings with Krull dimension one are shown to have closed left ideals in the J-adic topology. The radical of these rings also satisfies the AR property.