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

Pradip Girase, Vandeo C Borkar, Narayan Phadatare

Abstract


Let $M$ be a lattice module over a $C$-lattice $L$.  Let $Spec^{s}(M)$ be the collection of all second elements of $M$. In this paper, we consider a  topology on $Spec^{s}(M)$, 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 $Spec^{s}(M)$.  We investigate this topological space from the point of view of spectral spaces. We show that $Spec^{s}(M)$ is always $T_{0}-$space and  each finite irreducible closed subset of $Spec^{s}(M)$ has a generic point. 


Keywords


Second element, second spectrum, second classical Zariski topology, second radical element.

Subject classification

06D10; 06E10; 06F10.

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