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3. HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGSHashem Bordbar, Irina Cristea, Michal Novak, 2017, izvirni znanstveni članek Opis: 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.
Najdeno v: ključnih besedah
Ključne besede: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Objavljeno: 01.06.2017; Ogledov: 3779; Prenosov: 0
 Polno besedilo (138,31 KB) |
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8. Weak closure operations on ideals of BCK-algebrasHashem 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: ključnih besedah
Ključne besede: weak closure operation of finite type, (quasi-prime, positive implicative, commutative, implica- tive) weak closure operation.
Objavljeno: 01.12.2019; Ogledov: 2309; Prenosov: 0
Polno besedilo (629,86 KB) |
9. SEMI-PRIME CLOSURE OPERATIONS ON BCK-ALGEBRAHashem Bordbar, 2015, izvirni znanstveni članek Opis: 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.
Najdeno v: ključnih besedah
Ključne besede: BCI-algebra, BCK-algebra, closure operation, finite type closure operation, semi-prime closure operation.
Objavljeno: 01.12.2019; Ogledov: 2113; Prenosov: 0
Polno besedilo (194,69 KB) |
10. Quotient Structures of BCK/BCI-Algebras Induced by Quasi-Valuation MapsHashem Bordbar, Young Bae Jun, Seok Zun Song, 2018, izvirni znanstveni članek Opis: Relations between I-quasi-valuation maps and ideals in BCK/BCI
-algebras are investigated. Using the notion of an I-quasi-valuation map of a BCK/BCI-algebra, the quasi-metric space is induced, and several properties are investigated. Relations between the I-quasi-valuation map and the I-valuation map are considered, and conditions for an I-quasi-valuation map to be an I-valuation map are provided. A congruence relation is introduced by using the I-valuation map, and then the quotient structures are established and related properties are investigated. Isomorphic quotient BCK/BCI-algebras are discussed.
Najdeno v: ključnih besedah
Ključne besede: ideal, I-quasi-valuation map, I-valuation map, quasi-metric
Objavljeno: 01.12.2019; Ogledov: 2098; Prenosov: 0
Polno besedilo (261,47 KB) |
