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1.
HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS
Hashem bordbar, Irina Cristea, Michal Novak, 2017, original scientific article

Abstract: Inspired by the classical concept of height of a prime ideal in a ring, we proposed in a precedent paper the notion of height of a prime hyperideal in a Krasner hyperring. In this note we first generalize some results concerning the height of a prime hyperideal in a Noetherian Krasner hyperring, with the intent to extend this definition to the case of a general hyperideal in a such hyperring. The main results in this note show that, in a commutative Noetherian Krasner hyperring, the height of a minimal prime hyperideal over a proper hyperideal generated by n elements is less than or equal to n, the converse of this claim being also true. Based on this result, it can be proved that the height of such a prime hyperideal is limited by the height of a corresponding quotient hyperideal.
Found in: ključnih besedah
Keywords: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Published: 01.06.2017; Views: 2810; Downloads: 0
.pdf Fulltext (138,31 KB)

2.
Overview on the height of a hyperideal in Krasner hyperrings
Hashem bordbar, Irina Cristea, Michal Novak, 2017, published scientific conference contribution abstract

Found in: ključnih besedah
Keywords: Krasner hyperring, prime hyperideal, Noetherian hyperring
Published: 30.08.2017; Views: 2185; Downloads: 0
.pdf Fulltext (1,59 MB)

3.
Height of Prime Hyperideals in Krasner Hyperrings
Irina Cristea, Hashem Bordbar, 2017, original scientific article

Found in: ključnih besedah
Keywords: hyperring, prime/maximal hyperideal, dimension of a hyperring, height of a prime hyperideal
Published: 03.01.2018; Views: 2082; Downloads: 0
.pdf Fulltext (257,02 KB)

4.
A note on the support of a hypermodule
Hashem Bordbar, Michal Novak, Irina Cristea, 2020, original scientific article

Found in: ključnih besedah
Keywords: Krasner hyperring, prime/maximal hyperideal, length of hypermodules, annihilator of hypermodules, support of hypermodules
Published: 28.02.2019; Views: 1801; Downloads: 0
.pdf Fulltext (320,12 KB)

5.
A fuzzy application of the group Z_n to complete hypergroups
Irina Cristea, Elhan Hassani Sadrabadi, Bijan Davvaz, 2019, original scientific article

Found in: ključnih besedah
Keywords: complete hypergroup, intuitionistic fuzzy set, Wieferich prime
Published: 12.06.2019; Views: 1766; Downloads: 0
.pdf Fulltext (346,14 KB)

6.
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
Keywords: weak closure operation of finite type, (quasi-prime, positive implicative, commutative, implica- tive) weak closure operation.
Published: 01.12.2019; Views: 1393; Downloads: 0
.pdf Fulltext (629,86 KB)

7.
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
Keywords: BCI-algebra, BCK-algebra, closure operation, finite type closure operation, semi-prime closure operation.
Published: 01.12.2019; Views: 1320; Downloads: 0
.pdf Fulltext (194,69 KB)

8.
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
Keywords: non-zeromeet element, meet ideal, relative annihilator, semi-prime (resp., meet) weak closure operation.
Published: 02.12.2019; Views: 1292; Downloads: 0
.pdf Fulltext (267,87 KB)

9.
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
Keywords: (strong) quasi prime mapping, t-type weak closure operation, naive (sheer, tender, feeble tender) weak closure operation.
Published: 02.12.2019; Views: 1413; Downloads: 0
.pdf Fulltext (85,80 KB)

10.
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
Keywords: lower BCK-semilattice, relative annihilator, semi-prime closure operation, minimal prime decomposition, minimal prime factor
Published: 24.02.2020; Views: 1220; Downloads: 0
.pdf Fulltext (267,96 KB)

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