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1.
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.
Found in: osebi
Keywords: BCI-algebra, BCK-algebra, closure operation, finite type closure operation.
Published: 01.12.2019; Views: 1738; Downloads: 0
.pdf Fulltext (257,89 KB)

2.
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.
Found in: osebi
Keywords: weak closure operation of finite type, (quasi-prime, positive implicative, commutative, implica- tive) weak closure operation.
Published: 01.12.2019; Views: 1855; Downloads: 0
.pdf Fulltext (629,86 KB)

3.
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.
Found in: osebi
Keywords: Lower BCK-semilattice, meet set, meet ideal, plus ideal, meet operation, addition, semiring.
Published: 01.12.2019; Views: 1720; Downloads: 0
.pdf Fulltext (3,39 MB)

4.
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.
Found in: osebi
Keywords: Lower BCK-semilattice, relative annihilator, implicative ideal, positive implicative ideal, commutative ideal
Published: 01.12.2019; Views: 1902; Downloads: 0
.pdf Fulltext (207,08 KB)

5.
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.
Found in: osebi
Keywords: Left (resp., right) NI-ideal, translation, closed support, retrenched left (resp., right) NI-ideal.
Published: 02.12.2019; Views: 1632; Downloads: 0
.pdf Fulltext (118,91 KB)

6.
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.
Found in: osebi
Keywords: non-zeromeet element, meet ideal, relative annihilator, semi-prime (resp., meet) weak closure operation.
Published: 02.12.2019; Views: 1708; Downloads: 0
.pdf Fulltext (267,87 KB)

7.
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.
Found in: osebi
Keywords: (strong) quasi prime mapping, t-type weak closure operation, naive (sheer, tender, feeble tender) weak closure operation.
Published: 02.12.2019; Views: 1826; Downloads: 0
.pdf Fulltext (85,80 KB)

8.
Internal and external cubic subalgebras of BCK/BCI-algebras
Young Bae Jun, Mohammad Mehdi Zahedi, Hashem Bordbar, 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.
Found in: osebi
Keywords: subalgebra, internal cubic subalgebra, external cubic subalgebra
Published: 07.04.2021; Views: 804; Downloads: 0
.pdf Fulltext (362,75 KB)

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