1,109 research outputs found
A note on distributivity of the lattice of L-ideals of a ring
Many studies have investigated the lattice of fuzzy substructures of algebraic structures such as groups and rings. In this study, we prove that the lattice of L-ideals of a ring is distributive if and only if the lattice of its ideals is distributive, for an infinitely ?- distributive lattice L. © 2019 Hacettepe University. All rights reserved
Characterizations of hemirings by their -ideals
In this paper we characterize hemirings in which all -ideals or all fuzzy
-ideals are idempotent. It is proved, among other results, that every
-ideal of a hemiring is idempotent if and only if the lattice of fuzzy
-ideals of is distributive under the sum and -intrinsic product of
fuzzy -ideals or, equivalently, if and only if each fuzzy -ideal of
is intersection of those prime fuzzy -ideals of which contain it. We
also define two types of prime fuzzy -ideals of and prove that, a
non-constant -ideal of is prime in the second sense if and only if each
of its proper level set is a prime -ideal of
Fuzzy Toric Geometries
We describe a construction of fuzzy spaces which approximate projective toric
varieties. The construction uses the canonical embedding of such varieties into
a complex projective space: The algebra of fuzzy functions on a toric variety
is obtained by a restriction of the fuzzy algebra of functions on the complex
projective space appearing in the embedding. We give several explicit examples
for this construction; in particular, we present fuzzy weighted projective
spaces as well as fuzzy Hirzebruch and del Pezzo surfaces. As our construction
is actually suited for arbitrary subvarieties of complex projective spaces, one
can easily obtain large classes of fuzzy Calabi-Yau manifolds and we comment on
fuzzy K3 surfaces and fuzzy quintic three-folds. Besides enlarging the number
of available fuzzy spaces significantly, we show that the fuzzification of a
projective toric variety amounts to a quantization of its toric base.Comment: 1+25 pages, extended version, to appear in JHE
Fuzzy -ideals of hemirings
A characterization of an -hemiregular hemiring in terms of a fuzzy
-ideal is provided. Some properties of prime fuzzy -ideals of
-hemiregular hemirings are investigated. It is proved that a fuzzy subset
of a hemiring is a prime fuzzy left (right) -ideal of if and
only if is two-valued, , and the set of all in
such that is a prime (left) right -ideal of . Finally, the
similar properties for maximal fuzzy left (right) -ideals of hemirings are
considered
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