On Algebraic Multi-group Spaces¸linfan

A Smarandache multi-space is a union of n spaces A 1 , A 2 , · · · , A n with some additional conditions holding. Combining classical of a group with Smarandache multi-spaces, the conception of a multi-group space is introduced in this paper, which is a generalization of the classical algebraic structures, such as the group, filed, body, · · ·, etc.. Similar to groups, some characteristics of a multi-group space are obtained in this paper. The notion of multi-spaces is introduced by Smarandache in [5] under his idea of hybrid mathematics: combining different fields into a unifying field([6]). Today, this idea is widely accepted by the world of sciences. For mathematics, definite or exact solution under a given condition is not the only object for mathematician. New creation power has emerged and new era for the mathematics has come now. A Smarandache multi-space is defined by Definition 1.1 For any integer i, 1 ≤ i ≤ n let A i be a set with ensemble of