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Boolean atoms of Heyting algebras and their application. (Chinese. English summary) Zbl 1463.06041

Summary: A kind of direct product decomposition of Heyting algebras is obtained using the Boolean elements of Heyting algebras. Based on this decomposition of Heyting algebras, it is proved that a finite Heyting algebra can be obtained by substituting the atoms of a Boolean algebra with Heyting algebras. This conclusion reveals a kind of new relationship between Heyting algebras and Boolean algebras.

MSC:

06D20 Heyting algebras (lattice-theoretic aspects)
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