MATHEMATICA BOHEMICA, Vol. 128, No. 3, pp. 237-252 (2003)

Characterizations of the $0$-distributive semilattice

P. Balasubramani

P. Balasubramani, Department of Mathematics, Kongu Engineering College, Perundurai, Erode-638 052, India, e-mail:

Abstract: The $0$-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for $0$-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.

Keywords: semilattice, prime ideal, filter

Classification (MSC2000): 06A12, 06A99, 06B10, 06B99

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