21. A note on composition (m,n)-hyperringsMorteza Norouzi, Irina Elena Cristea, 2017, original scientific article Abstract: Based on the concepts of composition ring and composition hyperring, in this note we introduce the notion of composition structure for (m,n)-hyperrings and study the connections with composition hyperrings. Moreover we show that particular strong endomorphisms of (m,n)-hyperrings can determine the composition structure of such (m,n)-hyperrings. Finally, the three isomorphism theorems are presented in the case of composition (m, n)-hyperrings, showing that they are not a pure extension of those for composition hyperrings.
Keywords: n-hypergroup, (m, n)-hyperring, composition hyperideal
Published in RUNG: 13.07.2017; Views: 3938; Downloads: 0
This document has many files! More... |
22. |
23. HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGSHashem Bordbar, Irina Elena 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.
Keywords: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Published in RUNG: 01.06.2017; Views: 4513; Downloads: 0
This document has many files! More... |
