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Article

MSC: 06D99
Keywords:
0-distributive lattice; ideal; prime ideal; congruence relation; prime spectrum; minimal prime spectrum; maximal spectrum
Summary:
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 $.
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