摘要:

A necessary condition is given for a very wide separable p-group to be derermined by its n-socle (the set of elements of order at mostpn). A group G is very wide if it has a direct summand of final rank ‖G‖ which itself is a direct sum of cyclic groups. In the case, n=1 (as Shelat has shown)this condition is sufficient but for n>1 examples are given to show that this condition is not sufficient.

ISSN:0092-7872    

DOI:10.1080/00927879008823915

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Let R = k [y1,…,yt] be an affine domain (where k is a field) having krull dimension =n>0. Let I be a nonzero proper ideal of R and D be a subring of K. In section 1 we determine necessary and sufficient conditions in order that (S,R) is a 'lying over pair' where S = D+I. In section 2 we chaaracterize when S is a Maximal non-Noetherian subring of R. Further we determine when S is a maximal subring of R.

ISSN:0092-7872    

DOI:10.1080/00927879008823916

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823917

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823918

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823919

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823920

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

The descriptions of torsion theories and of torsion valued idempotent preradicals of abclian groups are well known. The description of all radicals of abelian groups is far from known and it is the purpose of this paper to demonstrat that the description of radicals whose values are torsion groups may he as complicated as the description of all torsion groups themselves. For each nou-negative integer n, we consider singly cogenerated radicals which fit between the radicals Pw+n+1and Pw+nshowing that there is a proper class of such radicals forming a chain therein. We also examine other intervals in the lattice of radicals showing either gaps or the existence of singly cogenerated radicals in these intervals.

ISSN:0092-7872    

DOI:10.1080/00927879008823921

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823922

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823923

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823924

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor