In this paper,bounded Heyting algebras and its ideals problem are studied by using the principle and meth-od of universal algebras and lattice-order theory.Firstly,the relationships among Ockham type bounded Heyting al-gebras,prelinearly bounded Heyting algebras and Boole algebras are discussed,and Some new properties of ideals in bounded Heyting algebras and Ockham bounded Heyting algebras are given.Secondly,the concept of prime ideal is in-troduced and its properties are investigated.The prime ideal theorem of Ockham bounded Heyting algebra is estab-lished.Some equivalent characterizations of prime ideals of prelinearly bounded Heyting algebras are obtained.Final-ly,for a given prelinearly bounded Heyting algebra(H,≤,→,0,1),a topology r is constructed on the set (F)ID(H)containing all of prime ideals in H by a natural way.Thus,the prime ideal spectrum space((F)ID(H),τ)of H is con-structed,and it is proved that this space is a compact Hausdorf space.
关键词
有界Heyting代数/Ockham型有界Heyting代数/素理想/谱空间
Key words
Bounded Heyting algebra/Ockham type bounded Heyting algebra/Prime ideal/Spectrum space
维普
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