Abstract
In this paper, we attempt to study the topological notions of multiplication module in the realm of purity. We let χ denote a collection of multiplication ideals of a ring R. We call an R module M to be χ-topological module (the topology being the Zariski topology on the prime spectrum of M) if, together with all the axiom of a topological space, it satisfies an additional condition that the collection of all the open sets is closed under arbitrary union. It is seen that over a Noetherian ring, a finitely generated multiplication module is a topological module if and only if it is a χ-topological module. Some important topological properties of a pure submodule of a multiplication module have also been studied.
2010 Mathematics subject classification: 16D40, 16D50.
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Purkayastha, S., Saikia, H.K. (2015). Characterization of χ-Topological Modules. In: Das, K., Deep, K., Pant, M., Bansal, J., Nagar, A. (eds) Proceedings of Fourth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 336. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2220-0_51
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DOI: https://doi.org/10.1007/978-81-322-2220-0_51
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