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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: ključnih besedah
Summary of found: ...article we study the (finite-type, cl-closed) closure operations on ideals of a BCK-algebra, with an...
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: ključnih besedah
Summary of found: ...Weak closure operation, which is more general form than closure...
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.
SEMI-PRIME CLOSURE OPERATIONS ON BCK-ALGEBRA
Hashem Bordbar, 2015, original scientific article

Abstract: In this paper we study the (good) semi-prime closure oper- ations on ideals of a BCK-algebra, lower BCK-semilattice, Noetherian BCK-algebra and meet quotient ideal and then we give several theorems that make different (good) semi-prime closure operations. Moreover, by giving some examples, we show that the given different notions are independent together, for instance, there is a semi-prime closure operation, which is not a good semi-prime. Finally by given the notion of “cf-Max X”, we prove that every member of “cf-Max X” is a prime ideal. Also, we conclude some more related results.
Found in: ključnih besedah
Summary of found: ...theorems that make different (good) semi-prime closure operations. Moreover, by giving some examples, we show...
Keywords: BCI-algebra, BCK-algebra, closure operation, finite type closure operation, semi-prime closure operation.
Published: 01.12.2019; Views: 1730; Downloads: 0
.pdf Fulltext (194,69 KB)

4.
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.
Found in: ključnih besedah
Summary of found: ...notion of tender and naive weak closure operation is introduced, and their relations and properties...
Keywords: zeromeet element, meet ideal, relative annihilator, (finite type, tender, naive) weak closure operation.
Published: 02.12.2019; Views: 1689; Downloads: 0
.pdf Fulltext (648,16 KB)

5.
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: ključnih besedah
Summary of found: ...notion of semi-prime (resp., meet) weak closure operation is introduced and related properties are investigated....
Keywords: non-zeromeet element, meet ideal, relative annihilator, semi-prime (resp., meet) weak closure operation.
Published: 02.12.2019; Views: 1707; Downloads: 0
.pdf Fulltext (267,87 KB)

6.
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: ključnih besedah
Summary of found: ...of all ideals, t- type weak closure operation, and tender (resp., naive, sheer, feeble tender)...
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)

7.
Primeness of Relative Annihilators in BCK-Algebra
Hashem Bordbar, 2020, original scientific article

Abstract: 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.
Found in: ključnih besedah
Summary of found: ...an ideal are considered. Using a semi-prime closure operation “cl”, we show that every minimal...
Keywords: lower BCK-semilattice, relative annihilator, semi-prime closure operation, minimal prime decomposition, minimal prime factor
Published: 24.02.2020; Views: 1683; Downloads: 0
.pdf Fulltext (267,96 KB)

8.
Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras
Hashem Bordbar, 2020, original scientific article

Found in: ključnih besedah
Keywords: zeromeet element, meet ideal, relative annihilator, semi-prime map, meet map, (semi-prime, meet) weak closure operation
Published: 21.04.2020; Views: 1587; Downloads: 0
.pdf Fulltext (221,66 KB)

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