Prime Separation Theorems for Semi Prime Ideals in Meet-Semilattices.

In this paper the authors study the Glivenko congruence θ in a meet semilattice S defined by "For an ideal J of S, a ≡ b(θ ) if and only if a ⋀ xϵ J is equivalent to b ⋀ xϵ J ; xϵ S ". They show that if S is directed above, then the quotient semilattice S/θ is also directed above. Moreover, if J is a semi prime ideal, then S/θ is a distributive semilattice with J = kerθ . Then they include a number of Prime Separation Theorems for semi prime ideals. [ABSTRACT FROM AUTHOR]