Interval Semirings

TL;DR

This book introduces and analyzes various algebraic structures called interval semirings, including new types like group and neutrosophic interval semirings, and explores their applications and problems.

Contribution

It provides the first comprehensive study of group, semigroup, loop, and groupoid interval semirings, expanding the theory of interval algebraic structures.

Findings

Introduction of group interval semirings and related structures

Analysis of algebraic properties of interval semirings

Applications of interval semirings in various contexts

Abstract

This book has seven chapters. In chapter one we give the basics needed to make this book a self contained one. Chapter two introduces the notion of interval semigroups and interval semifields and are algebraically analysed. Chapter three introduces special types of interval semirings like matrix interval semirings and interval polynomial semirings. Chapter four for the first time introduces the notion of group interval semirings, semigroup interval semirings, loop interval semirings and groupoid interval semirings and these structures are studied. Interval neutrosophic semirings are introduced in chapter five. Applications of these structures are given in chapter six. The final chapter suggests around 120 problems for the reader.