Fuzzy ideals in laskerian rings
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Date
2013
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematical Society of Serbia
Abstract
We introduce strongly primary fuzzy ideals and strongly irreducible fuzzy ideals
in a unitary commutative ring and fixed their role in a Laskerian ring. We established that: A
finite intersection of prime fuzzy ideals (resp. primary fuzzy ideals, irreducible fuzzy ideals and
strongly irreducible fuzzy ideals) is a prime fuzzy ideal (resp. primary fuzzy ideal, irreducible
fuzzy ideal and strongly irreducible fuzzy ideal). We also find that, a fuzzy ideal of a ring is
prime if and only if it is semiprime and strongly irreducible. Furthermore we characterize that:
(1) Every nonzero fuzzy ideal of a one dimensional Laskerian domain can be uniquely expressed
as a product of primary fuzzy ideals with distinct radicals, (2) A unitary commutative ring is
(strongly) Laskerian if and only if its localization is (strongly) Laskerian with respect to every
fuzzy ideal.
Description
Keywords
Mathematics, Prime Fuzzy Ideal, Primary Fuzzy Ideal, Irreducible Fuzzy Ideal
Citation
Matematički Vesnik 65, 1 (2013), 74–81