Browsing by Author "Tariq Shah"

Now showing 1 - 3 of 3
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    Factorization properties and chain conditions on ideals: A linkage
    (2012) Saeed, Muhammad; Tariq Shah; Inayatur-Rehman; Waheed Ahmad Khan
    The purpose of this study is to find relationship among the various domains. In particular, the domains possessing factorization properties and the domains which hold different chain conditions on ideals.
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    Fuzzy ideals in laskerian rings
    (Mathematical Society of Serbia, 2013) Tariq Shah; Muhammad Saeed
    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.
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    On fuzzy ideals in rings and anti-homomorphism
    (International Mathematical Forum, 2012) Tariq Shah; Saeed, Muhammad
    We investigate anti- homomorphic images and pre images of semiprime, strongly primary, irreducible and strongly irreducible fuzzy ideals of a ring. We also prove that: For a surjective anti-homomorphism f : R → R/, if every fuzzy ideal of R is f-invariant and has a fuzzy primary (respectively, strongly primary) decomposition in R, then every fuzzy ideal of R/ has a fuzzy primary (respectively, strongly primary) decompsition in R/.