Abstract/Details

SOME INJECTIVE CLASSES

GOETERS, HERMAN PAT. 
 University of Connecticut ProQuest Dissertations Publishing,  1984. 8416089.

Abstract (summary)

All groups are assumed to be in the category of torsion free abelian groups of finite rank with homomorphisms. Let TF be this category of groups. We consider three natural methods of generating injective classes of groups. One method produces all cotorison theories in TF which we characterize. The work done is similar to L. Salce's work. Other work done is similar to work done by W. Wickless and C. Vinsonhaler.

We use these injective classes to prove the following. Let I(C(H)) denote the injective class generated by H. We prove: (a) The reduced groups in I(C({G})) are G-projective if G (TURNEQ) X(,1) (CRPLUS)...(CRPLUS) X(,n) where each X(,i) is rank 1 and if i (NOT=) j then {p (VBAR) pX(,i) (NOT=) X(,i)} (INTERSECT) {p (VBAR) pX(,j) (NOT=) X(,j)} = (SLASHCIRC). (b)

(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)

is the class of groups Y, Y (TURNEQ) X(,n(,1)) (CRPLUS)...(CRPLUS) X(,n(,k)) (CRPLUS) Q('n) for some integers n(,1),...,n(,k),n, if

(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)

is a set of rank 1 groups with {p (VBAR) pX(,j) (NOT=) X(,j)} (INTERSECT) {p (VBAR) pX(,i) (NOT=) X(,i)} = (SLASHCIRC) if i (NOT=) j.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
SOME INJECTIVE CLASSES
Author
GOETERS, HERMAN PAT
Number of pages
80
Degree date
1984
School code
0056
Source
DAI-B 45/04, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-204-57482-3
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8416089
ProQuest document ID
303287254
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303287254/abstract