## Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2012

#### Abstract

In this book the authors introduce a new type of dual numbers called special dual like numbers. These numbers are constructed using idempotents in the place of nilpotents of order two as new element. That is x = a + bg is a special dual like number where a and b are reals and g is a new element such that g2 =g. The collection of special dual like numbers forms a ring. Further lattices are the rich structures which contributes to special dual like numbers. These special dual like numbers x = a + bg; when a and b are positive reals greater than or equal to one we see powers of x diverge on; and every power of x is also a special dual like number, with very large a and b. On the other hand if a and b are positive reals lying in the open interval (0, 1) then we see the higher powers of x may converge to 0. Another rich source of idempotents is the Neutrosophic number I, as I2 = I. We build several types of finite or infinite rings using these Neutrosophic numbers.

#### Publisher

Zip Publishing, Ohio

#### ISSN

978-1-59973-185-8

#### Language (ISO)

English

#### Keywords

dual like numbers, neutrosophic logic, algebraic structures

#### Recommended Citation

W.B. Vasantha Kandasamy & F. Smarandache. Special Dual like Numbers and Lattices. Ohio: Zip Publishing, 2012.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.

#### Included in

Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Applied Mathematics Commons, Discrete Mathematics and Combinatorics Commons, Dynamical Systems Commons, Logic and Foundations Commons, Number Theory Commons