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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