Special Dual Like Numbers and Lattices

In this book we define x = a+bg to be a special dual like number, where a, b are reals and g is a new element such that g^2 = g. The new element which is idempotent can be got from Z_n or from lattices or from linear operators. Mixed dual numbers are constructed using dual numbers and special dual like numbers. Neutrosophic numbers are a natural source of special dual like numbers, since they have the form a+bI, where I = indeterminate and I^2 = I.