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1.
刘仲奎 《数学杂志》1995,15(4):429-435
本文引入了相对平坦左S-系的概念,用来给出了强忠实右S-系的特征刻划。  相似文献   

2.
强忠实右S-系   总被引:3,自引:0,他引:3  
本文引入了相对平坦左S-系的概念,用来给出了强忠实右S-系的特征刻划。  相似文献   

3.
刘仲奎 《数学杂志》1999,19(3):339-344
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。  相似文献   

4.
正则左S-系是von neumann正则半群的自然推广,逆左S-系是逆半群的自然扩广,作为左逆半群的自然推广,本文引入了L-逆左系的概念,并用来刻画了几类幺半群,如左逆幺半群,逆幺半群,adequate幺半群等。  相似文献   

5.
正则左S-系是von Neumann正则半群的自然推广,逆左S-系是逆半群的自然推广.作为左逆半群的自然推广,本文引入了L-逆左系的概念,并用来刻画了几类幺半群,如左逆幺半群,逆幺半群,adequate幺半群等.  相似文献   

6.
本论文考虑了所有强平坦右S-系是正则系的幺半群的刻画,证明了所有强平坦右S-系是正则S-系当且仅当S是右PSF幺半群并且S的每一个左coilpasible子幺半群包含左零元.该结果对Kilp和Knauer在文献[7]中的问题给出了一个新的回答.  相似文献   

7.
弱交换富足序半群(Ⅰ)   总被引:5,自引:0,他引:5  
高振林 《数学学报》2001,44(4):693-700
本文将序半群上的 Green’s-关系推广为 Green’s*一关系.给出主序(左、右)*-理想、主序*-滤特征描述和弱交换富足序半群的特征.用这些特征证明了一类弱交换富足序半群的结构定理:若序半群S满足 ,则S是弱交换富足序半群当且仅当S是左(右)单序半群{(e)(S)}的半格.  相似文献   

8.
刘仲奎 《数学杂志》1996,16(2):151-156
设S是幺半群,在右S-系范畴Act-S中,有两种纯性的概念,分别被Normak,Gould和Renshaw所研究。我们分别称之为NG-纯性和R-纯性,本文考虑NG-纯性和R-纯性的关系。我们证明了NG-纯性蕴含R-纯性,并且给出例子说明反过来是不对的,最后我们引入了关系正合序列的概念,并用来研究循环系的R-纯循环子系的性质。  相似文献   

9.
设S是么半群,在右S-系范畴Act-S中,有两种纯性的概念,分别被Normak,Gould和Renshaw所研究.我们分别称之为NG-纯性和R-纯性.本文考虑NG-纯性和R-纯性的关系.我们证明了NG-纯性蕴含R-纯性,并且给出例子说明反过来是不对的.最后我们引入了关系正合序列的概念,并用来研究循环系的R-纯循环子系的性质.  相似文献   

10.
由Ramamurthi和Ming的两个公开问题所推动,本文证明了如下结果:(1)如果R是MELT,SF-环,那么R是正则环;(2)如果R是MELT,左CE-内射,右SF-环,那么R是具有有界指数的左和右自内射正则,左和右V-环.这就给出了Ramamurthi和Ming两个公开问题的部分回答.  相似文献   

11.
C(P)系对幺半群的刻画   总被引:1,自引:1,他引:0  
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.  相似文献   

12.
M. Sedaghatjoo  V. Laan 《代数通讯》2013,41(11):4019-4030
For a monoid S, the set S × S equipped with the componentwise right S-action is called the diagonal act of S and is denoted by D(S). A monoid S is a left PP (left PSF) monoid if every principal left ideal of S is projective (strongly flat). We shall call a monoid S left P(P) if all principal left ideals of S satisfy condition (P). We shall call a monoid S weakly left P(P) monoid if the equalities as = bs, xb = yb in S imply the existence of r ∈ S such that xar = yar, rs = s. In this article, we prove that a monoid S is left PSF if and only if S is (weakly) left P(P) and D(S) is principally weakly flat. We provide examples showing that the implications left PSF ? left P(P) ? weakly left P(P) are strict. Finally, we investigate regularity of diagonal acts D(S), and we prove that for a right PP monoid S the diagonal act D(S) is regular if and only if every finite product of regular acts is regular. Furthermore, we prove that for a full transformation monoid S = 𝒯 X , D(S) is regular.  相似文献   

13.
设S是幺半群,x,x2,…∈S且满足xi+1i=xi,i=1,2……y是S中的任意元素,记H={(yxi,xi)|i=1,2,…}.设ρ(H)是S的由H生成的最小右同余,本文证明了S/ρ(H)是平坦右S-系.  相似文献   

14.
15.
Guba  V. S. 《Semigroup Forum》2021,103(1):286-290
Semigroup Forum - It is known that if a cancellative monoid M is left amenable then the monoid ring K[M] satisfies the Ore condition, that is, there exist nontrivial common right multiples for the...  相似文献   

16.
Let M be a cancellative monoid such that the monoid ring ℤM has no zero divisors. We show that if the monoid consisting of all elements of ℤM with strictly positive coefficients has nonzero common right multiples, then M is left amenable.  相似文献   

17.
Monoids and acts which may have zero elements are considered. In Section 1 we construct a O-wreath product of monoids. In 2 we prove the theorem that the endomorphism monoid of a free act over a monoid with zero can be represented as a O-wreath product. Considering monoids with tero we are interested in their annihilator properties. In 3 we give necessary and sufficient conditions for a O-wreath product of monoids to be a right (left) Baer (Rickart) monoid. In 4 we obtain as a consequence corresponding conditions for the endomorphism monoid of a free act over a monoid with zero.  相似文献   

18.
《代数通讯》2013,41(6):2447-2459
The aim of this paper is to study a class of rpp semigroups, namely the perfect rpp semigroups. We obtain some characterization theorems for such semigroups. In particular, the spined product structure of perfect rpp semigroups is established. As an application of spined product structure, we prove that a perfect rpp semigroup is a strong semilattice of left cancellative planks. By a left cancellative plank, we mean a product of a left cancellative monoid and a rectangular band. Thus, the work of J.B. Fountain on C-rpp semigroups is further developed.

  相似文献   

19.
右消去幺半群、左正则带和左正则型A幺半群   总被引:2,自引:0,他引:2  
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.  相似文献   

20.
张霞  陈裕群  王燕鸣 《东北数学》2006,22(3):357-369
Let S be a semigroup with zero and an S-act be a centered left S-act. This paper is devoted to the study of chain conditions on PS-acts. We prove that a PS-act having finite decomposition has ACC (DCC) on all subacts if it has ACC (DCC) on essential subacts. Moreover, a PS-act with ACC (DCC) on essential subacts has ACC (DCC) on all subacts if and only if it has finite decomposition. We characterize the structure of a PS-act and generalize some results of the Goldie dimension and semisimple S-acts.  相似文献   

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