In this book the authors introduce a new notion called special quasi dual number, x = a + bg.
Among the reals – 1 behaves in this way, for (– 1)2 = 1 = – (– 1). Likewise –I behaves in such a way (– I)2 = – (– I). These special quasi dual numbers can be generated from matrices with entries from 1 or I using only the natural product ×n. Another rich source of these special quasi dual numbers or quasi special dual numbers is Zn, n a composite number. For instance 8 in Z12 is such that 82 = 64 = – 8(mod 12) = 4(mod 12). In chapter two we introduce the notion of special quasi dual numbers. The notion of higher dimensional special quasi dual numbers are introduced in chapter three of this book. We using the dual numbers and special dual like numbers with special quasi dual numbers construct three types of mixed special quasi numbers and discuss their properties.
Zip Publishing, Ohio
special quasi dual number, number theory, algebraic structures, neutrosophic logic
W.B. Kandasamy & F. Smarandache. Special Quasi Dual Numbers and Groupoids. Ohio: Zip Publishing, 2012.
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