The theory of algebraic hyperstructures, in particular the theory of Krasner hyperrings, has seen a spectacular development in the last 20 years, which is why a book dedicated to the study of these is so vital. Krasner hyperrings are a generalization of hyperfields, introduced by Krasner in order to study complete valued fields. A Krasner hyperring (R, +, .) is an algebraic structure, where (R, +) is a canonical hypergroup, (R, .) is a semigroup having zero as a bilaterally absorbing element and the multiplication is distributive with respect to the hyperoperation +.

Krasner Hyperring Theory presents an elaborate study on hyperstructures, particularly Krasner hyperrings, across 10 chapters with extensive examples. It contains the results of the authors, but also of other researchers in the field, focusing especially on recent research. This book is especially addressed to doctoral students or researchers in the field, as well as to all those interested in this interesting part of algebra, with applications in other fields.

Contents:

• Canonical Hypergroups


• Introduction to Krasner Hyperrings


• Homomorphisms and Isomorphisms


• Generalizations of Hyperideals


• Lower and Upper Approximations in Krasner Hyperrings


• Derived Hyperstructures from Hyperconics


• Fundamental Relations on Krasner Hyperrings


• Some Special Hyperrings


• Differential Krasner Hyperrings


• Ordered Krasner Hyperrings

Readership: This book will be of interest to libraries, graduate students, academics and researchers in the field and in related fields.

Key Features:

• Both authors are well-known experts in hypergroups and hyperrings


• Discusses topics on Krasner hyperrings, with most results on Krasner hyperrings collected in this single book


• This monograph is the first book on this theory