On subtractive varieties. IV: Definability of principal ideals
[For parts I--III see Zbl 0799.08010, Zbl 0902.08010 and Zbl 0906.08005, respectively.] The concept of ideal in universal algebra was introduced by the second author. This paper deals with equationally definable principal ideals (EDPI) in the so-called subtractive varieties (alias varieties permutable at 0). The authors introduce one variety of generalized Hilbert algebras and prove that this is a paradigm of a subtractive variety with EDPI. Then they deal with principal ideal operations and with the cases of meet and join of principal ideals being equationally definable.
scientific article; zbMATH DE number 1407081