Geodesic
Reticulation of a 0-distributive Lattice
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 54 (2015) no. 1, pp. 121-128 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A congruence relation $\theta $ on a 0-distributive lattice is defined such that the quotient lattice $L/\theta $ is a distributive lattice and the prime spectrum of $L$ and of $L/\theta $ are homeomorphic. Also it is proved that the minimal prime spectrum (maximal spectrum) of $L$ is homeomorphic with the minimal prime spectrum (maximal spectrum) of $L/\theta $.
A congruence relation $\theta $ on a 0-distributive lattice is defined such that the quotient lattice $L/\theta $ is a distributive lattice and the prime spectrum of $L$ and of $L/\theta $ are homeomorphic. Also it is proved that the minimal prime spectrum (maximal spectrum) of $L$ is homeomorphic with the minimal prime spectrum (maximal spectrum) of $L/\theta $.
Classification : 06D99
Keywords: 0-distributive lattice; ideal; prime ideal; congruence relation; prime spectrum; minimal prime spectrum; maximal spectrum 
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Pawar, Y. S. Reticulation of a 0-distributive Lattice. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 54 (2015) no. 1, pp. 121-128. http://geodesic.mathdoc.fr/item/AUPO_2015_54_1_a8/

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