Geodesic
On disjoint sums in the lattice of linear topologies
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 3-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $M$ be a vector space over a skew-field equipped with the discrete topology, $\mathcal L(M)$ be the lattice of all linear topologies on $M$ ordered by inclusion, and $\tau_*,\tau_0,\tau_1\in\mathcal L(M)$. We write $\tau_1=\tau_*\sqcup\tau_0$ or say that $\tau_1$ is a disjoint sum of $\tau_*$ and $\tau_0$ if $\tau_1=\inf\{\tau_0,\tau_*\}$ and $\sup\{\tau_0,\tau_*\}$ is the discrete topology. Given $\tau_1,\tau_0\in\mathcal L(M)$, we say that $\tau_0$ is a disjoint summand of $\tau_1$ if $\tau_1=\tau_*\sqcup\tau_0$ for a certain $\tau_*\in\mathcal L(M)$. Some necessary and some sufficient conditions are proved for $\tau_0$ to be a disjoint summand of $\tau_1$. 
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V. I. Arnautov; K. M. Filippov. On disjoint sums in the lattice of linear topologies. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 3-18. http://geodesic.mathdoc.fr/item/FPM_2003_9_1_a0/

[1] Arnautov V. I., Glavatski S. T., Mikhalev A. V., Introduction to the theory of topological rings and modules, Marcel Dekker, New York, 1996 | MR | Zbl

[2] Arnautov V. I., Filippov K. M., “On coverings in the lattice of module topologies”, Buletinul Academiei de Ştiinţe a Republicii Moldova Matematica, 1999, no. 2(30), 7–18 | MR

[3] Birkhoff G., Lattice theory, Providence, Rhode Island, 1967 | MR

[4] Warner S., Topological rings, North-Holland, Amsterdam, 1993 | MR | Zbl