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arXiv · 1305.4578

On Topological Lattices and an Application to First Submodules

Jawad Abuhlail·Christian Lomp
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Abstract

We introduce the notion of a (strongly) topological lattice $\mathcal{L}=(L,\wedge ,\vee)$ with respect to a subset $X\subsetneqq L;$ aprototype is the lattice of (two-sided) ideals of a ring $R,$ which is(strongly) topological with respect to the prime spectrum of $R.$ We investigate and characterize (strongly) topological lattices. Given a non-zero left $R$-module $M,$ we introduce and investigate the spectrum $\mathrm{Spec}^{\mathrm{f}}(M)$ of \textit{first submodules} of $M.$ We topologize $\mathrm{Spec}^{\mathrm{f}}(M)$ and investigate the algebraic properties of $_{R}M$ by passing to the topological properties of the associated space.

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Jawad Abuhlail, Christian Lomp. 2013-05-20. On Topological Lattices and an Application to First Submodules. https://doi.org/10.1142/s0219498816500468

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