Volume 16, Number 1, January 2022, 29-58.
https://doi.org/10.52547/cgasa.16.1.29
A new approach to tensor product of
hypermodules
Seyed Shahin Mousavi
Abstract. As an essential tool in homological algebra, tensor products
play a basic role in classifying and studying modules. Since hypermodules
are generalization of modules, it is important to generalize the concept of
the tensor products of modules to the hypermodules. In this paper, in order
to achieve this goal, we present a more general form of the definition of
hypermodule. Based on this new definition, some of the required concepts
and properties have been studied. By obtaining a free object in the category
of hypermodules, the notion of tensor product of hypermodules is provided
and some of its properties are studied.
1 Introduction and preliminaries
In the 8th Congress of Scandinavian Mathematicians in 1934, Marty intro-
duced the hyperstructure theory, see [14], and stated that, the hypergroup
is the generalization of groups. Marty showed that the characteristics of
hypergroup can be used in solving some problems of groups, algebraic func-
tions, and rational fractions. Surveys of the theory can be found in [8, 10].
Keywords : Hypermodule, free object, tensor product.
Mathematics Subject Classification [2010]: 20N20.
Received: 29 April 2021, Accepted: 28 July 2021.
ISSN: Print 2345-5853, Online 2345-5861.
© Shahid Beheshti University
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