A note on composition (m, n)-hyperrings

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 a 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.

Composition Vector Spaces as a New Type of Tri-Operational Algebras

“…The study in this direction was opened by Cristea and Jancic-Rasovic [10] by defining the composition hyperrings, which better describe the structure of the hyperrings of polynomials [11]. This work was then continued in two directions: the study of the (m, n)-hyperrings endowed with a composition operation [12] and the study of the hyperrings endowed with a composition, i.e., an n-ary hyperoperation [13]. Combining these two directions, one may study the composition (m, n, k)-hyperrings [14], that are (m, n)-hyperrings endowed with a k-ary composition hyperoperation.…”

Normal hyperideals in Krasner (m, n)-hyperrings

“…N-ary hyperstructures, in particular n-ary hypergroups, were introduced by Davvaz and Vougiouklis [13] and represented a generalization of both hypergroups and n-ary groups, defined by Dornte [14] in 1928. Several authors have worked on this new topic of research, for instance (m, n)-hyperrings and (m, n)-hypermodules were introduced and studied in [1], [2], [3], [5], [8], [9], [11], [16], [17], [18], [20], [21], [22], [23] and [24].…”

Distributive and Dual Distributive Elements in Hyperlattices

“…Some applications can be found also in e.g. in [4,5,8,10,16,17]. The theory of hyperlattices was introduced by Konstantinidou in 1977 [13].…”