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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: 3349; Prenosov: 0
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Opis: The notion of tender and naive weak closure operation is introduced, and their relations and properties are investigated. Using a weak closure operation "d" and an ideal A of a lower BCK-semilattice X with the greatest element 1, a new ideal K of X containing the ideal Acl of X is established. Using this ideal K, a new function clt : I(X) → I(X); A → K is given, and related properties are considered. We show that if "cl" is a tender (resp., naive) weak closure operation on I(X), then so are "clt" and clf.
Ključne besede: zeromeet element, meet ideal, relative annihilator, (finite type, tender, naive) weak closure operation.
Objavljeno v RUNG: 02.12.2019; Ogledov: 3424; Prenosov: 0
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Ključne besede: BCK–algebra, ideal, lower BCK–semilattice, relative annihilator
Objavljeno v RUNG: 12.02.2018; Ogledov: 4175; Prenosov: 0
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