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

Z. Belali | Zendy; S. M. Anvariyeh | Zendy; S. Mirvakili | Zendy

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

Author(s) -

Z. Belali,

S. M. Anvariyeh,

S. Mirvakili

Publication year - 2011

Publication title -

tamkang journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 18

eISSN - 0049-2930

pISSN - 2073-9826

DOI - 10.5556/j.tkjm.42.2011.870

Subject(s) - mathematics , generalization , free product , finitely generated abelian group , combinatorics , pure mathematics , free group , discrete mathematics , algebra over a field , group (periodic table) , mathematical analysis , chemistry , organic chemistry

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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