On the Zariski topology over an $L$-module $M$

Authors: FETHİ ÇALLIALP, GÜLŞEN ULUCAK, ÜNSAL TEKİR

Abstract: Let $L$ be a multiplicative lattice and $M$ be an $L$-module. In this study, we present a topology said to be the Zariski topology over $\sigma (M),$ the collection of all prime elements of an $L$-module $M.$ We research some results on the Zariski topology over $\sigma (M).$ We show that the topology is a $T_{0}$-space and a $T_{1}$-space under some conditions. Some properties and results are studied for the topology over $\sigma (L)$, the collection of all prime elements of a multiplicative lattice $L.$

Keywords: Lattice, lattice module, prime element, Zariski topology

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