The normal conjugation on the polynumber set. 2004jby  Garasko G.I., Pavlov D.G.
The polynumber set is an example of linear space with several polylinear forms. The concept of normal conjunction is introduced on the set of nondegenerated nnumbers. The normal conjunction is a (n1)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 nnumber 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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