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3. Tender and naive weak closure operations on lower BCK-semilattices.Hashem Bordbar, 2018, original scientific article Abstract: 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.
Keywords: zeromeet element, meet ideal, relative annihilator, (finite type, tender, naive) weak closure operation.
Published in RUNG: 02.12.2019; Views: 3465; Downloads: 0
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4. Semiring structures based on meet and plus ideals in lower BCK-semilatticesHashem Bordbar, 2017, original scientific article Abstract: The notion of the meet set based on two subsets of a lower BCK-semilattice X is introduced, and related properties are investigated. Conditions for the meet set to be a (positive implicative, commutative, implicative) ideal are discussed. The meet ideal based on subsets, and the plus ideal of two subsets in a lower BCK-semilattice X are also introduced, and related properties are investigated. Using the meet operation and addition, the semiring structure is induced.
Keywords: Lower BCK-semilattice, meet set, meet ideal, plus ideal, meet operation, addition, semiring.
Published in RUNG: 01.12.2019; Views: 3323; Downloads: 0
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