On Algebraic Multi-Group Spaces

A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,\mathrm{.}\mathrm{.}\mathrm{.},A_n$ 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, $\mathrm{.}\mathrm{.}\mathrm{.}$, etc… Similar to groups, some characteristics of a multi-group space are obtained in this paper.