Branch Mathematics and Statistics 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 International 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
