Document Type : Review paper

Authors

1 Department of Pure Mathematics‎, ‎Calcutta University‎, ‎35-Ballygaunge Circular Road‎, ‎Kolkata-700019‎, ‎India

2 Department of Mathematics‎, ‎Adamas University‎, ‎Barasat-Barrackpore Road‎, ‎Jagannathpur‎, ‎Kolkata‎, ‎India

Abstract

‎Quasi module is a new algebraic structure‎, ‎based on module‎, ‎which is composed of a semigroup structure and a partial order accompanied with an external ring multiplication‎. ‎We proposed this structure in our paper \cite{qmod} while we were studying the hyperspace $ \com{M}{} $ consisting of all nonempty compact subsets of a topological module $ M $ over some topological ring $ R $‎. ‎Quasi module can be considered as a generalisation of module in some sense‎. ‎In the present paper we have defined topological quasi module and given some examples of it‎. ‎We have shown that the Cartesian product of arbitrary family of topological quasi modules is again a topological quasi module over some topological unitary ring‎. ‎Finally we have defined projective system of topological quasi modules and projective limit of this system‎. ‎We have proved various topological properties of the projective limit of a projective system‎.

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Main Subjects

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