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

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Published: Mar 1, 2011
DOI: https://doi.org/10.5556/j.tkjm.42.2011.870
Keywords:
Canonical $m-$ary hypergroup Krasner $(m n)-$ary hyperring free $(m n)-$ary hypermodules.

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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.

Abstract

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. https://doi.org/10.5556/j.tkjm.42.2011.870
Issue
Vol. 42 No. 1 (2011)
Section
Papers
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