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1.
Internal and external cubic subalgebras of BCK/BCI-algebras
Hashem Bordbar, Mohammad Mehdi Zahedi, Young Bae Jun, 2021, original scientific article

Abstract: A characterization of cubic subalgebra is established. The notion of internal and external cubic subalgebra in BCK\BCI-algebra, and several properties are investigated. The R-union, R-intersection, P-union, and P-intersection of internal and external cubic subalgebras in BCK=BCI-algebra are discussed.
Keywords: subalgebra, internal cubic subalgebra, external cubic subalgebra
Published in RUNG: 07.04.2021; Views: 2031; Downloads: 0
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2.
WEAK CLOSURE OPERATIONS WITH SPECIAL TYPES IN LOWER BCK-SEMILATTICES
Hashem Bordbar, Young Bae Jun, 2017, original scientific article

Abstract: The notions of (strong) quasi prime mapping on the set of all ideals, t- type weak closure operation, and tender (resp., naive, sheer, feeble tender) weak closure operation are introduced, and their relations and properties are investigated. Conditions for a weak closure operation to be of t-type are provided. Given a weak closure operation, conditions for the new weak closure operation to be of t-type and to be a naive (sheer, feeble tender) weak closure operation are considered. We show that the new weak closure operation is the smallest tender weak closure operation containing the given weak closure operation.
Keywords: (strong) quasi prime mapping, t-type weak closure operation, naive (sheer, tender, feeble tender) weak closure operation.
Published in RUNG: 02.12.2019; Views: 3016; Downloads: 0
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3.
Semi-prime and meet weak closure operations in lower BCK-semilattices
Hashem Bordbar, Mohammad Mehdi Zahedi, 2017, original scientific article

Abstract: The notion of semi-prime (resp., meet) weak closure operation is introduced and related properties are investigated. Characterizations of a semi-prime (resp. meet) closure operation are discussed. Examples show that the notion of semi-prime weak closure operation is independent of the notion of meeting weak closure operation.
Keywords: non-zeromeet element, meet ideal, relative annihilator, semi-prime (resp., meet) weak closure operation.
Published in RUNG: 02.12.2019; Views: 2874; Downloads: 0
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4.
IDEALS OF IS-ALGEBRAS BASED ON N-STRUCTURES
Hashem Bordbar, Mohammad Mehdi Zahedi, Young Bae Jun, 2018, original scientific article

Abstract: The notion of a left (resp., right) NI-ideal is introduced, and related properties are investigated. Characterizations of a left (resp., right) NI-ideal are considered. Translations of a left (resp., right) NI-ideal are studied. We show that the homomorphic image (preimage) of a left (resp., right) NI-ideal is a left (resp., right) NI-ideal. The notion of retrenched left (resp., right) NI-ideals is introduced, and their properties are investigated.
Keywords: Left (resp., right) NI-ideal, translation, closed support, retrenched left (resp., right) NI-ideal.
Published in RUNG: 02.12.2019; Views: 2755; Downloads: 0
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5.
Weak closure operations on ideals of BCK-algebras
Hashem Bordbar, 2017, original scientific article

Abstract: Weak closure operation, which is more general form than closure operation, on ideals of BCK- algebras is introduced, and related properties are investigated. Regarding weak closure operation, finite type and (strong) quasi-primeness are considered. Also positive implicative (resp., commutative and implicative) weak closure operations are discussed.
Keywords: weak closure operation of finite type, (quasi-prime, positive implicative, commutative, implica- tive) weak closure operation.
Published in RUNG: 01.12.2019; Views: 3262; Downloads: 0
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6.
A Finite type Closure Operations on BCK-algebras
Hashem Bordbar, 2016, original scientific article

Abstract: In this article we study the (finite-type, cl-closed) closure operations on ideals of a BCK-algebra, with an emphasis on structural properties. Also we give several theorems that make different closure operations, especially on a quotient and Noetherian BCK-algebra. In particular, we show that the intersection and union (by imposing some additional conditions) of closure operations is a closure operation and every closure operation is a finite type on any finitely generated ideal. Moreover by given the notions of residuated quotient ideals and the meet of two ideals, we conclude some related results.
Keywords: BCI-algebra, BCK-algebra, closure operation, finite type closure operation.
Published in RUNG: 01.12.2019; Views: 2857; Downloads: 0
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7.
Semiring structures based on meet and plus ideals in lower BCK-semilattices
Hashem 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: 2828; Downloads: 0
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8.
Relative annihilators in lower BCK-semilattices
Hashem Bordbar, Mohammad Mehdi Zahedi, Young Bae Jun, 2017, original scientific article

Abstract: As a generalization of annihilators, the notion of a relative annihilator is introduced, and their properties are investigated. Conditions for a relative annihilator to be an implicative (resp., positive implicative, commutative) ideal are discussed.
Keywords: Lower BCK-semilattice, relative annihilator, implicative ideal, positive implicative ideal, commutative ideal
Published in RUNG: 01.12.2019; Views: 3209; Downloads: 0
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