Projective system of topological quasi modules

Journal of Linear and Topological Algebra

دوره 10، شماره 03، آذر 2021، صفحه 205-216   

نوع مقاله: Review paper

نویسندگان

S. Jana¹؛ S. Mazumder^{* 2}

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

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

چکیده

‎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.

کلیدواژه‌ها

Quasi module؛ topological quasi module؛ projective system؛ projective limit

مراجع

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[4] S. Mazumder, Sandip Jana, Exact sequence on quasi module, Southeast Asian Bulletin of Mathematics. 41 (2017), 525-533.

[5] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182.

[6] L. Nachbin, Topology And Order, D. Van Nostrand Company, 1965.