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TitleFrames of ideals of commutative f-rings
AuthorSithole, Maria Lindiwe
SubjectFrame
SubjectCompact normal frame
SubjectCoherent frame
SubjectD-ideal
SubjectD-elements
SubjectL-ideal
SubjectRadical ideal
SubjectFunctor
SubjectF-ring
SubjectZero-dimensional
SubjectStrongly normal
Subject512.64
SubjectCommutative rings
SubjectCommutative algebra
SubjectRing (algebra)
Date2019-03-12T07:39:27Z
Date2019-03-12T07:39:27Z
Date2018-09
TypeDissertation
Format1 online resource ( 51 leaves)
AbstractIn his study of spectra of f-rings via pointfree topology, Banaschewski [6] considers lattices of l-ideals, radical l-ideals, and saturated l-ideals of a given f-ring A. In each case he shows that the lattice of each of these kinds of ideals is a coherent frame. This means that it is compact, generated by its compact elements, and the meet of any two compact elements is compact. This will form the basis of our main goal to show that the lattice-ordered rings studied in [6] are coherent frames. We conclude the dissertation by revisiting the d-elements of Mart nez and Zenk [30], and characterise them analogously to d-ideals in commutative rings. We extend these characterisa-tions to algebraic frames with FIP. Of necessity, this will require that we reappraise a great deal of Banaschewski"s work on pointfree spectra, and that of Mart nez and Zenk on algebraic frames.
AbstractMathematical Sciences
AbstractMSc. (Mathematics)
IdentifierSithole, Maria Lindiwe (2018) Frames of ideals of commutative f-rings, University of South Africa, Pretoria,
Identifierhttp://hdl.handle.net/10500/25328