Open AccessFree 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