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1.
A Finite type Closure Operations on BCK-algebras
Hashem Bordbar, 2016, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: BCI-algebra, BCK-algebra, closure operation, finite type closure operation.
Objavljeno: 01.12.2019; Ogledov: 1669; Prenosov: 0
.pdf Polno besedilo (257,89 KB)

2.
Weak closure operations on ideals of BCK-algebras
Hashem Bordbar, 2017, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: weak closure operation of finite type, (quasi-prime, positive implicative, commutative, implica- tive) weak closure operation.
Objavljeno: 01.12.2019; Ogledov: 1771; Prenosov: 0
.pdf Polno besedilo (629,86 KB)

3.
Semiring structures based on meet and plus ideals in lower BCK-semilattices
Hashem Bordbar, 2017, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: Lower BCK-semilattice, meet set, meet ideal, plus ideal, meet operation, addition, semiring.
Objavljeno: 01.12.2019; Ogledov: 1634; Prenosov: 0
.pdf Polno besedilo (3,39 MB)

4.
Relative annihilators in lower BCK-semilattices
Hashem Bordbar, Mohammad Mehdi Zahedi, Young Bae Jun, 2017, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: Lower BCK-semilattice, relative annihilator, implicative ideal, positive implicative ideal, commutative ideal
Objavljeno: 01.12.2019; Ogledov: 1798; Prenosov: 0
.pdf Polno besedilo (207,08 KB)

5.
IDEALS OF IS-ALGEBRAS BASED ON N-STRUCTURES
Hashem Bordbar, Mohammad Mehdi Zahedi, Young Bae Jun, 2018, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: Left (resp., right) NI-ideal, translation, closed support, retrenched left (resp., right) NI-ideal.
Objavljeno: 02.12.2019; Ogledov: 1558; Prenosov: 0
.pdf Polno besedilo (118,91 KB)

6.
Semi-prime and meet weak closure operations in lower BCK-semilattices
Hashem Bordbar, Mohammad Mehdi Zahedi, 2017, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: non-zeromeet element, meet ideal, relative annihilator, semi-prime (resp., meet) weak closure operation.
Objavljeno: 02.12.2019; Ogledov: 1631; Prenosov: 0
.pdf Polno besedilo (267,87 KB)

7.
WEAK CLOSURE OPERATIONS WITH SPECIAL TYPES IN LOWER BCK-SEMILATTICES
Hashem Bordbar, Young Bae Jun, 2017, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: (strong) quasi prime mapping, t-type weak closure operation, naive (sheer, tender, feeble tender) weak closure operation.
Objavljeno: 02.12.2019; Ogledov: 1751; Prenosov: 0
.pdf Polno besedilo (85,80 KB)

8.
Internal and external cubic subalgebras of BCK/BCI-algebras
Young Bae Jun, Mohammad Mehdi Zahedi, Hashem Bordbar, 2021, izvirni znanstveni članek

Opis: 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.
Najdeno v: osebi
Ključne besede: subalgebra, internal cubic subalgebra, external cubic subalgebra
Objavljeno: 07.04.2021; Ogledov: 734; Prenosov: 0
.pdf Polno besedilo (362,75 KB)

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