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Opis: Conditions that are necessary for the relative annihilator in lower BCK-semilattices to be a prime ideal are discussed. Given the minimal prime decomposition of an ideal A, a condition for any prime ideal to be one of the minimal prime factors of A is provided. Homomorphic image and pre-image of the minimal prime decomposition of an ideal are considered. Using a semi-prime closure operation “cl”, we show that every minimal prime factor of a cl-closed ideal A is also cl-closed.
Ključne besede: lower BCK-semilattice, relative annihilator, semi-prime closure operation, minimal prime decomposition, minimal prime factor
Objavljeno v RUNG: 24.02.2020; Ogledov: 3682; Prenosov: 0
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Opis: In this paper we study the (good) semi-prime closure oper- ations on ideals of a BCK-algebra, lower BCK-semilattice, Noetherian BCK-algebra and meet quotient ideal and then we give several theorems that make different (good) semi-prime closure operations. Moreover, by giving some examples, we show that the given different notions are independent together, for instance, there is a semi-prime closure operation, which is not a good semi-prime. Finally by given the notion of “cf-Max X”, we prove that every member of “cf-Max X” is a prime ideal. Also, we conclude some more related results.
Ključne besede: BCI-algebra, BCK-algebra, closure operation, finite type closure operation, semi-prime closure operation.
Objavljeno v RUNG: 01.12.2019; Ogledov: 3655; Prenosov: 0
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