Spelling suggestions: "subject:"ideals (algebra)"" "subject:"ideals (álgebra)""
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Sperner properties of the ideals of a Boolean latticeMcHard, Richard William. January 2009 (has links)
Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Title from first page of PDF file (viewed March 11, 2010). Available via ProQuest Digital Dissertations. Includes bibliographical references (p. 170-172). Also issued in print.
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Problems in computational algebra and integer programming /Bogart, Tristram, January 2007 (has links)
Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 132-136).
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Ideals, varieties, and Groebner basesAhlgren, Joyce Christine 01 January 2003 (has links)
The topics explored in this project present and interesting picture of close connections between algebra and geometry. Given a specific system of polynomial equations we show how to construct a Groebner basis using Buchbergers Algorithm. Gröbner bases have very nice properties, e.g. they do give a unique remainder in the division algorithm. We use these bases to solve systems of polynomial quations in several variables and to determine whether a function lies in the ideal.
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Concerning ideals of pointfree function ringsIghedo, Oghenetega 11 1900 (has links)
We study ideals of pointfree function rings. In particular, we study the lattices of z-ideals
and d-ideals of the ring RL of continuous real-valued functions on a completely regular
frame L. We show that the lattice of z-ideals is a coherently normal Yosida frame; and
the lattice of d-ideals is a coherently normal frame. The lattice of z-ideals is demonstrated
to be
atly projectable if and only if the ring RL is feebly Baer. On the other hand, the
frame of d-ideals is projectable precisely when the frame is cozero-complemented.
These ideals give rise to two functors as follows: Sending a frame to the lattice of
these ideals is a functorial assignment. We construct a natural transformation between the
functors that arise from these assignments. We show that, for a certain collection of frame
maps, the functor associated with z-ideals preserves and re
ects the property of having a
left adjoint.
A ring is called a UMP-ring if every maximal ideal in it is the union of the minimal
prime ideals it contains. In the penultimate chapter we give several characterisations for
the ring RL to be a UMP-ring. We observe, in passing, that if a UMP ring is a Q-algebra,
then each of its ideals when viewed as a ring in its own right is a UMP-ring. An example
is provided to show that the converse fails.
Finally, piggybacking on results in classical rings of continuous functions, we show that,
exactly as in C(X), nth roots exist in RL. This is a consequence of an earlier proposition
that every reduced f-ring with bounded inversion is the ring of fractions of its bounded
part relative to those elements in the bounded part which are units in the bigger ring. We
close with a result showing that the frame of open sets of the structure space of RL is isomorphic to L. / Mathematical Sciences / Mathematics / D.Phil. (Mathematics)
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Maximally Prüfer ringsUnknown Date (has links)
In this dissertation, we consider six Prufer-like conditions on acommutative ring R. These conditions form a hierarchy. Being a Prufer ring is not a local property: a Prufer ring may not remain a Prufer ring when localized at a prime or maximal ideal. We introduce a seventh condition based on this fact and extend the hierarchy. All the conditions of the hierarchy become equivalent in the case of a domain, namely a Prufer domain. We also seek the relationship of the hierarchy with strong Prufer rings. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2015 / FAU Electronic Theses and Dissertations Collection
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Concerning ideals of pointfree function ringsIghedo, Oghenetega 11 1900 (has links)
We study ideals of pointfree function rings. In particular, we study the lattices of z-ideals
and d-ideals of the ring RL of continuous real-valued functions on a completely regular
frame L. We show that the lattice of z-ideals is a coherently normal Yosida frame; and
the lattice of d-ideals is a coherently normal frame. The lattice of z-ideals is demonstrated
to be
atly projectable if and only if the ring RL is feebly Baer. On the other hand, the
frame of d-ideals is projectable precisely when the frame is cozero-complemented.
These ideals give rise to two functors as follows: Sending a frame to the lattice of
these ideals is a functorial assignment. We construct a natural transformation between the
functors that arise from these assignments. We show that, for a certain collection of frame
maps, the functor associated with z-ideals preserves and re
ects the property of having a
left adjoint.
A ring is called a UMP-ring if every maximal ideal in it is the union of the minimal
prime ideals it contains. In the penultimate chapter we give several characterisations for
the ring RL to be a UMP-ring. We observe, in passing, that if a UMP ring is a Q-algebra,
then each of its ideals when viewed as a ring in its own right is a UMP-ring. An example
is provided to show that the converse fails.
Finally, piggybacking on results in classical rings of continuous functions, we show that,
exactly as in C(X), nth roots exist in RL. This is a consequence of an earlier proposition
that every reduced f-ring with bounded inversion is the ring of fractions of its bounded
part relative to those elements in the bounded part which are units in the bigger ring. We
close with a result showing that the frame of open sets of the structure space of RL is isomorphic to L. / Mathematical Sciences / D.Phil. (Mathematics)
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Topics on z-ideals of commutative ringsTlharesakgosi, Batsile 02 1900 (has links)
The first few chapters of the dissertation will catalogue what is known regarding z-ideals in
commutative rings with identity. Some special attention will be paid to z-ideals in function
rings to show how the presence of the topological description simplifies z-covers of arbitrary
ideals. Conditions in an f-ring that ensure that the sum of z-ideals is a z-ideal will be given.
In the latter part of the dissertation I will generalise a result in higher order z-ideals and
introduce a notion of higher order d-ideals / Mathematical Sciences / M. Sc. (Mathematics)
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