The normal conjugation on the poly-number set.
2004jby | Garasko G.I., Pavlov D.G.

The poly-number set is an example of linear space with several poly-linear forms. The concept of normal conjunction is introduced on the set of non-degenerated n-numbers. The normal conjunction is a (n-1)-nary operation. It is commutative for each argument, but generally not associative. For complex and hyperbolic numbers the generalized conjunction is equivalent to usual one. The normal conjunction may be applied for scrutiny of algebraic and geometric structures of n-number coordinate spaces. It is also useful for introducing such concepts like scalar product and angular characteristics of two and more numbers (vectors)

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