Branch Mathematics and Statistics Faculty and Staff Publications
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.
Educational Publisher Inc., Ohio
algebra, neutrosophic logic, mathematics
W.B. Vasantha Kandasamy & F. Smarandache (eds.) Algebraic Structures on Real and Neutrosophic Semi Open Squares. Ohio: Education Publishing, 2014
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