Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Book
Publication Date
2014
Abstract
Here for the first time we introduce the semi open square using modulo integers. Authors introduce several algebraic structures on them. These squares under addition modulo ‘n’ is a group and however under product this semi open square is only a semigroup as under the square has infinite number of zero divisors. Apart from + and we define min and max operation on this square. Under min and max operation this semi real open square is a semiring. It is interesting to note that this semi open square is not a ring under + and since a (b + c) ≠ a b + a c in general for all a, b and c in that semi open square. So we define the new type of ring call pseudo ring. Finally we define S-vector spaces and S-pseudo linear algebras using them.
Publisher
Educational Publisher Inc., Ohio
ISSN
978-1-59973-291-6
Language (ISO)
English
Keywords
algebra, neutrosophic logic, mathematics
Recommended Citation
W.B. Vasantha Kandasamy & F. Smarandache (eds.) Algebraic Structures on Real and Neutrosophic Semi Open Squares. Ohio: Education Publishing, 2014
Creative Commons License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.
Included in
Algebra Commons, Applied Mathematics Commons, Discrete Mathematics and Combinatorics Commons, Logic and Foundations Commons
