Free and cyclic canonical (m,n)- ary hypermodules - Belali, Z.; Anvariyeh, S. M.; Mirvakili, S. (Tamkang Journal of Mathematics, 2011)
In this paper, the class of free and cyclic canonical (m,n)-ary hypermodules over Krasner (m,n)-ary hyperrings is defined. Free canonical (m,n)-ary hypermodules are a generalization of free canonical hypermodules and a generalization of free modules. Also, several properties are found. In addition, we introduce the concepts of a free basis and a free (m,n)-hypermodules as a free object in the category of (m,n)-hypermodules and prove some results in this respect. Finally, we obtain some results and relations among a finitely generated torsion free and a free (m,n)-hypermodule.