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Reticulation of a 0-distributive Lattice

Y. S. Pawar — 2015

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A congruence relation θ on a 0-distributive lattice is defined such that the quotient lattice L / θ is a distributive lattice and the prime spectrum of L and of L / θ 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 / θ .

α -ideals and annihilator ideals in 0-distributive lattices

Y. S. Pawar;  S. S. Khopade — 2010

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In a 0-distributive lattice sufficient conditions for an α -ideal to be an annihilator ideal and prime ideal to be an α -ideal are given. Also it is proved that the images and the inverse images of α -ideals are α -ideals under annihilator preserving homomorphisms.

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