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http://dx.doi.org/10.11568/kjm.2020.28.3.439

SECOND CLASSICAL ZARISKI TOPOLOGY ON SECOND SPECTRUM OF LATTICE MODULES  

Girase, Pradip (Department of Mathematics, K. K. M. College)
Borkar, Vandeo (Department of Mathematics, Yeshwant Mahavidyalaya)
Phadatare, Narayan (Department of Mathematics Savitribai Phule Pune University)
Publication Information
Korean Journal of Mathematics / v.28, no.3, 2020 , pp. 439-447 More about this Journal
Abstract
Let M be a lattice module over a C-lattice L. Let Specs(M) be the collection of all second elements of M. In this paper, we consider a topology on Specs(M), called the second classical Zariski topology as a generalization of concepts in modules and investigate the interplay between the algebraic properties of a lattice module M and the topological properties of Specs(M). We investigate this topological space from the point of view of spectral spaces. We show that Specs(M) is always T0-space and each finite irreducible closed subset of Specs(M) has a generic point.
Keywords
Second element; second spectrum; second classical Zariski topology; second radical element;
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