Prime Separation Theorems for Semi Prime Ideals in Meet-Semilattices

摘要

In this paper the authors study the Glivenko congruence θin a meet semilattice S defined by "For an ideal J of S, )(θba≡if and only if Jxa∈∧is equivalent to Jxb∈∧; Sx∈". They show that if S is directed above, then the quotient semilattice θSis also directed above. Moreover, if J is a semi prime ideal, then θSis a distributive semilattice with θker=J. Then they include a number of Prime Separation Theorems for semi prime ideals.