Algebraic Structures using [0,n)

Authors

Florentin Smarandache, University of New MexicoFollow
Vasantha KandasamyFollow

Document Type

Book

Publication Date

2013

Abstract

In this book authors for the first time introduce a new method of building algebraic structures on the interval [0, n). This study is interesting and innovative. However, [0, n) is a semigroup under product, × modulo n and a semigroup under min or max operation. Further [0, n) is a group under addition modulo n. We see [0, n) under both max and min operation is a semiring. [0, n) under + and × is not in general a ring. We define S = {[0, n), +, ×} to be a pseudo special ring as the distributive law is not true in general for all a, b  S. When n is a prime, S is defined as the pseudo special interval domain which is of infinite order for all values of n, n a natural integer.

Several special properties about these structures are studied and analyzed in this book. Certainly these new algebraic structures will find several application in due course of time. All these algebraic structures built using the interval [0, n) is of infinite order.

Publisher

Educational Publisher Inc., Ohio

ISSN

978-1-59973-248-0

Language (ISO)

English

Keywords

algebraic structures, interval groups, neutrosophic logic

Recommended Citation

W.B. Vasantha Kandasamy & F. Smarandache. Algebraic Structures using [0,n). Ohio: Educational Publisher Inc., 2013.

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