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IMI/Publicaţii/BASM/Ediţii/BASM n.2(87), 2018/

Quotient Structure and Chain Conditions on Quasi Modules

Authors: Sandip Jana, Supriyo Mazumder

Abstract

Quasi module is an axiomatisation of the hyperspace structure based on a module. We initiated this structure in our paper \cite{qmod-iso}. It is a generalisation of the module structure in the sense that every module can be embedded into a quasi module and every quasi module contains a module. The structure of quasi module is a conglomeration of a commutative semigroup with an external ring multiplication and a compatible partial order. In the entire structure partial order has an intrinsic effect and plays a key role in any development of the theory of quasi modules. In the present paper we have discussed the quotient structure of a quasi module by introducing a congruence suitably. Also we introduce the concept of chain conditions on quasi modules and prove some theorems related to chain conditions.

Department of Pure Mathematics
University of Calcutta
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Kolkata-700019, India
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