Green's theories and coextensions

Date Issued
June 1, 1980
Author(s)
Cripps, Alfred H.
Advisor(s)
J. H. Carruth
Additional Advisor(s)
Charles E. Clark
Robert J.
C. P. H.
Permanent URI
Abstract
In Chapter II, the categories of Green's pairs and Green's theories are defined. The general properties of these categories are investigated, and the two categories are shown to be equivalent. Also the category of Green's pairs are related to the usual Green's quasi-orders while relationships between Green's pairs and other generalizations of Green's relations are developed. This is done by performing a construction using a free semigroup to obtain a coextension with the desired properties. An example is given to show that Green's pairs are more general than the other generalizations studied. Also specific types of Green's pairs and their properties are investigated.

In Chapter III, some of the results of Chapter II are applied in the study of quasi-orders under ≤(H) . For each L [R] quasi-order under ≤(H) , it is shown that there corresponds a functor from ≤L [≤R] into Mon while for each L [R] equivalence under ≤(H) , it is shown that there corresponds a functor from ≤L [≤R] into Grp. Also the R equivalences under ≤(H) (viewed as a lattice) are shown to be isomorphic to a lattice contained in the functors from ≤R to Grp.

Also in Chapter III, ≤(G) and ≤(S) coextensions are defined for the category ḠP̄. Then the results in the first part of the chapter are used to establish a construction principle using functors from ≤L and ≤R into Mon. Using this construction principle one is able to construct (reconstruct) all ≤(G) and ≤(S) coextensions (in the category ḠP̄).

Degree
Doctor of Philosophy
Major
Mathematics
File(s)
Thumbnail Image
Name

Thesis80b.C756.pdf

Size

3.04 MB

Format

Unknown

Checksum (MD5)

30172ca67de3983e171a9d2632f38e96