Regular Parameter Elements and Regular Local Hyperrings

Abstract

Inspired by the concept of regular local rings in classical algebra, in this article we initiate the study of the regular parameter elements in a commutative local Noetherian hyperring. These elements provide a deep connection between the dimension of the hyperring and its primary hyperideals. Then, our study focusses on the concept of regular local hyperring R, with maximal hyperideal M, having the property that the dimension of R is equal to the dimension of the vectorial hyperspace MM2 over the hyperfield RM. Finally, using the regular local hyperrings, we determine the dimension of the hyperrings of fractions.

BCK codes

“…Moreover, using the notations and ideas of this article, the codes generated from hyperstructures, such as hyper BC K -algebra, hyper modules and etc., can be presented. For more details about hyperstructures, please refer to Bordbar and Cristea (2021, 2012; Bordbar et al ( , 2020c.…”

Hypergroup Theory and Algebrization of Incidence Structures

“…A large number of papers has been published on the hyperfields and hyperrings, starting from the pioneer work of J. Mittas [37][38][39][40][41][42][43][44] and continuing with a plenitude of researchers, such as Ch. Massouros [29,35,[45][46][47][48][49][50][51], A. Nakassis [36], G. Massouros [50][51][52][53][54], R. Rota [55,56], S. Jančic-Rašović [57][58][59], I. Cristea [58][59][60][61][62][63][64], H. Bordbar [59][60][61], M. Kankaraš [62], V. Vahedi et al [63][64][65], M. Jafarpour et al [63][64][65][66], A. Connes and C. Consani [67,68], O. Viro [69,70], R. Ameri, M. Eyvazi and S. Hoskova-Mayero...…”

Hyperstructure Theory Applied to BF-Algebras

“…Several authors later investigated hyperstructure in various algebraic structures, such as hyperfields [11], n-ary semihypergroups [12], ordered semihypergroups [13], Γsemihypergroups [14], etc. More hyperstructure theories are studied in [15][16][17][18][19][20][21][22][23].…”