所有循环平坦系满足条件（P）的PSF幺半群

本文讨论所有循环平坦系满足条件（Ｐ）的幺半群的“元素－－理想”特征问题,该问题至今仍未获解决,在Ｓ是左ＰＳＦ幺半群的条件下,本文证明了所有循环平坦右Ｓ－系满足条件（Ｐ）当且仅当Ｓ的任意元ｘ或者是右可消元,或者是右零元,当且仅当对Ｓ的任意真右理想Ｉ,或存在ａ∈Ｉ－Ｉａ,或Ｉ中的所有元素均为右零元,该结果改进并推广了「４」、「７」、「８」、「１５」中的部分结果。     

幺半群上的广义内射S-系(英文)

本文考虑拟内射、伪内射、核内射以及支内射S-系的性质,重点讨论这些广义内射S-系的上的线性方程组的性质.例如,A是核内射S-系当且仅当A的任意收缩核B上的任意A-相容线性方程组在B上是可解的;A是支内射S-系当且仅当同构于A的任一分支的S-系B上的任意A-相容线性方程组在B上是可解的.进而讨论了伪内射、核内射以及支内射S-系的融合余积的性质.最后给出了一个充分条件,基于此条件核内射和支内射S-系是等价的.     

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．     

n-正则幺半群的平坦性刻画

本文研究了主弱平坦性质的推广问题.利用张量积相等的等式组,以及同调分类方法,获得了对广义正则的幺半群的刻画结果,推广了关于正则幺半群刻画的主要的结果.     

右消去幺半群、左正则带和左正则型A幺半群

本文利用右消去幺半群,左正则带建立了真左正则型A幺半群．在证明了任一左正则型A幺半群均有P－覆盖后,给出P－覆盖的结构．     

C(P)系对幺半群的刻画

设S是幺半群.本文介绍并研究了正则右系的一个推广.一个右S-系A称为C(P)系,如果A的所有循环子系满足条件(P).本文证明了右C(P)系形成了右S-系的一个新的类,同时,C(P)性质为幺半群同调分类研究提供了新思路.     

图的强收缩核与图的强自同态幺半群的正则性

本文研究图及其强自同态幺半群．首先刻画了图的强自同态幺半群的正则元，然后给出了此幺半群正则的充要条件．这推广了［１］和［２］中关于有限图的强自同态幺半群正则的结果．     

正则系对有局部单位半群的刻画

借助酉系范畴中的正则对象研究了有局部单位半群的同调分类问题.通过研究正则对象中元素的性质,建立了正则性质与余直积以及正合序列之间的联系;通过探索正则对象与主弱平坦对象以及投射对象的关系,给出了有局部单位半群同调分类的刻画.     

图的强化缩核与图的强自同态幺半群的正则性

本文研究图及其强自同态幺半群，首先刻画了图的强自同态幺半群的正则元，然后给出了此幺半群正则的充要条件，这推广了（１）和（２）中关于有限图的强自同态幺半群正则的结果。     

关于所有子模是纯子模的平坦模

引进了一新模类-完全平坦模(每一个商模平坦).并得到了:令M是平坦左R-模,RM是完全平坦模当且仅当RM的所有子模是纯的当且仅当每一个右R-模A是M-平坦的.同时本文用完全平坦模刻画了V.N.正则环.     

On Retractable S-Acts

In this paper we introduce a class of right S-acts called retractable S-acts which are right S-acts with homomorphisms into their all subacts. We also give some classifications of monoids by comparing such acts with flatness properties.     

On Monoids for Which all Condition (P) Acts are Strongly Flat

In this article, we continue to investigate the monoids over which all right S-acts satisfying condition (P) are strongly flat, and we obtain some new classes of monoids, thereby extending all previous results in this area.     

Strongly Flat Modules over Matlis Domains

Strongly flat modules were introduced by Bazzoni–Salce [3 Bazzoni , S. , Salce , L. ( 2003 ). Almost perfect domains . Colloq. Math. 95 : 285 – 301 .[Crossref] , [Google Scholar]] and used to characterize almost perfect domains. Here we wish to study strongly flat modules, more generally, over Matlis domains; these are integral domains R such that the field of quotients Q has projective dimension 1. In Section 2, criteria are proved for strong flatness. We also prove that over arbitrary domains, strongly flat submodules of projective modules are projective (Theorem 3.2), in particular, strongly flat ideals are projective (Corollary 3.4) and use these results to show that the strongly flat dimension (which makes sense over Matlis domains) coincides with the projective dimension whenever it is > 1.     

Strongly Flat and Condition (P) Covers of Acts Over Monoids

In this article we characterize monoids over which every right S-act has a strongly flat (condition (P)) cover. Similar to the perfect monoids, such monoids are characterized by condition (A) and having strongly flat (condition (P)) cover for each cyclic right S-act. We also give a new characterization for perfect monoids as monoids over which every strongly flat right S-act has a projective cover.     

Globals of Completely Regular Monoids

An element of a semigroup S is called irreducible if it cannot be expressed as a product of two elements in S both distinct from itself. In this paper we show that the class C of all completely regular...     

On Strongly Copure Flat Modules and Copure Flat Dimensions

Let R be a left coherent ring. We first prove that a right R-module M is strongly copure flat if and only if Ext ⁱ (M, C) = 0 for all flat cotorsion right R-modules C and i ≥ 1. Then we define and investigate copure flat dimensions of left coherent rings. Finally, we give some new characterizations of n-FC rings.     

关于GP-V-环与强正则环的刻划

The purpose of this paper is to characterize strongly regular rings via MERT rings and weakly one-sided ideals. Many important equivalent conditions on strongly regular rings are shown.     

幂等元生成子半群为完全正则半群的拟完全正则半群

论文主要刻画了幂等元生成子半群为完全正则半群的拟完全正则半群. 并讨论了满足该类半群的一些子类.