W. B. Vasantha Kandasamy, Florentin Smarandache
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. We define the new type of ring call pseudo ring. Finally we define S-vector spaces and S-pseudo linear algebras using them. This concept will in due course of time find lots of applications. Several open problems are suggested for interested researchers.
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