关键词: 极小素理想, 零化子, [&alpha, ]-理想, 拓扑空间

Abstract: The equivalence of minimal prime ideals and minimal lattice prime ideals in lattice implication algebras is proved, then the reciprocal representation theorem of minimal prime ideals and annihilators is provided. The concept of [α]-ideal is proposed and several equivalent characterizations are established, also prime ideals being[α]-ideals are proved. The set [Sα(L)] of all prime [α]-ideals being a compact Stone space is proved, moreover the sufficient and necessary conditions for [Sα(L)] being [T1,T2] spaces respectively are obtained.

Key words: minimal prime ideal, annihilator, [α]-ideal, topology space