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: osebi
Ključne besede: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Objavljeno: 01.06.2017; Ogledov: 2370; Prenosov: 0
Polno besedilo (138,31 KB)
Further results on (∈, ∈)-neutrosophic subalgebras and ideals in BCK/BCI-algebrasHashem Bordbar
, Florentin Smarandache
, Young Bae Jun
, G Muhiuddin
, 2018, izvirni znanstveni članek
Opis: Characterizations of an (∈, ∈)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (∈, ∈)-neutrosophic ideal. The re- lation between (∈, ∈)-neutrosophic ideal and (∈, ∈)-neutrosophic subalgebra in a BCK-algebra is discussed. Conditions for an (∈∈)-neutrosophic subalgebra to be a (∈, ∈)-neutrosophic ideal are provided. Using a collection of ideals in a BCK/BCI-algebra, an (∈, ∈)-neutrosophic ideal is established. Equivalence relations on the family of all (∈, ∈)-neutrosophic ideals are introduced, and re- lated properties are investigated.
Najdeno v: osebi
Ključne besede: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal.
Objavljeno: 01.12.2019; Ogledov: 1002; Prenosov: 0
Polno besedilo (6,02 MB)