Free and cyclic canonical $\bf{(m,n)-}$ ary hypermodules


  • Z. Belali Department ofMathematics, Yazd University, Yazd, Iran.
  • S. M. Anvariyeh Department ofMathematics, Yazd University, Yazd, Iran.
  • S. Mirvakili Mathematics Department, Payame Noor University, 19395-4697 Tehran, I. R. of IRAN.



Canonical $m-$ary hypergroup, Krasner $(m, n)-$ary hyperring, free $(m, n)-$ary hypermodules.


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.


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How to Cite

Belali, Z., Anvariyeh, S. M., & Mirvakili, S. (2011). Free and cyclic canonical $\bf{(m,n)-}$ ary hypermodules. Tamkang Journal of Mathematics, 42(1), 105–118.