ISSN:0092-7872    

DOI:10.1080/00927879308824588

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

摘要:

In [4], Macaulay proved that μ(mI) ≥Q(μ(I)) ≥ μ(I) for any homogeneous idealIink[X1, …,Xn] with minimal generators of a single degree wheremis the homogeneous maximal ideal (X1, …,Xn) andQis the function called the Binomial Expansion basen- 1. The inequelity can be generalised to the case of torsion-fre modules with generators of a single degree. The proof follows the lines of Robbiano [5]. A family of counterexamples to μ(mI) ≥ μ(I) in whichIhas minimal generators of just two different degrees is given.

ISSN:0092-7872    

DOI:10.1080/00927879308824589

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

摘要:

A moduleMRis defined to be strongly compressible (or SC for short) if for every essential submoduleNofM, there existsX⊆E(M)such thatM⊆X≅N. We show that a ring R is semiprime right Goldie iffRRis SC module iff every right ideal ofRis SC module iff every submodule of each progenerator of Mod-Ris SC module. As corollaries of this result, we obtain some new module-theoretic characterizations of semiprime Goldie rings, prime (right) Goldie rings and Prüfer rings, etc., etc.,respectively. And the characterization theorem of semiprime Goldie rings of López-Permouth, Rizvi and Yousif by using weakly-injective modules can be regarded as a corollary of our results.

ISSN:0092-7872    

DOI:10.1080/00927879308824590

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824591

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824592

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824567

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor