Date of Award
2009
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
Abstract
The structure of minimal zero-dimensional extension of rings with Noetherian spectrum in which zero is a primary ideal and with at most one prime ideal of height greater than one is determined. These rings include K[[X,T]] where K is a field and Dedenkind domains, but need not be Noetherian nor integrally closed. We show that for such a ring R there is a one-to-one correspondence between isomorphism classes of minimal zero-dimensional extensions of R and sets M, where the elements of M are ideals of R primary for distinct prime ideals of height greater than zero. A subsidiary result is the classification of minimal zero-dimensional extensions of general ZPI-rings.
Extent
v, 43 p. : ill.
Recommended Citation
Chiorescu, Marcela, "Minimal zero-dimensional extensions" (2009). Electronic Theses and Dissertations 2000 - 2009. 1727.
https://digitalcommons.fau.edu/etd_general_5/1727
Identifier
FADT210447
Comments
by Marcela Chiorescu.|Thesis (Ph.D.)--Florida Atlantic University, 2009.|Includes bibliography.|Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.|by Marcela Chiorescu.