1. HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGSHashem 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: 3581; Downloads: 0 Fulltext (138,31 KB) |
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6. Weak closure operations on ideals of BCK-algebrasHashem 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: 2130; Downloads: 0 Fulltext (629,86 KB) |
7. SEMI-PRIME CLOSURE OPERATIONS ON BCK-ALGEBRAHashem 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: 1968; Downloads: 0 Fulltext (194,69 KB) |
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9. WEAK CLOSURE OPERATIONS WITH SPECIAL TYPES IN LOWER BCK-SEMILATTICESHashem 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: 2070; Downloads: 0 Fulltext (85,80 KB) |
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