Korean J. Math. Vol. 28 No. 3 (2020) pp.439-447
DOI: https://doi.org/10.11568/kjm.2020.28.3.439

Second classical Zariski topology on second spectrum of lattice modules

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Published: Sep 30, 2020
Keywords:
Second element, second spectrum, second classical Zariski topology, second radical element.
Mathematics Subject Classification:
06D10, 06E10, 06F10.

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Pradip Girase
Department of Mathematics, K. K. M. College Manwath, Dist-Parbhani(M.S.)-431505, India.
Vandeo C Borkar
Department of Mathematics, Yeshwant college, Nanded. 431602, India.
Narayan Phadatare
Department of Mathematics, Savitribai Phule Pune University, Pune(M.S.), India.

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.



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