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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: 1735; 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: ...properties are investigated. Regarding weak closure operation, finite type and (strong) quasi-primeness are considered. Also...
Keywords: weak closure operation of finite type, (quasi-prime, positive implicative, commutative, implica- tive) weak closure operation.
Published: 01.12.2019; Views: 1852; 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: ...BCI-algebra, BCK-algebra, closure operation, finite type closure operation, semi-prime closure operation.... ...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: 1723; 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: ...zeromeet element, meet ideal, relative annihilator, ( finite type, tender, naive) weak closure operation....
Keywords: zeromeet element, meet ideal, relative annihilator, (finite type, tender, naive) weak closure operation.
Published: 02.12.2019; Views: 1686; Downloads: 0
.pdf Fulltext (648,16 KB)

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