This paper deals with notions of (equational) definability of principal ideals in subtractive varieties. These notions are first characterized in several different ways. The strongest notion (EDPI) is then further investigated. We introduce the variety of MINI algebras (a generalization of Hilbert algebras) and we show that they are a paradigm for subtractive EDPI varieties. Finally we deal with principal ideal operations, and in particular with the cases of meet and join of principal ideals being equationally definable.
Agliano', P., Ursini, A. (1997). On subtractive varieties IV: Definability of principal ideals. ALGEBRA UNIVERSALIS, 38(3), 355-389 [10.1007/s000120050059].
On subtractive varieties IV: Definability of principal ideals
AGLIANO', PAOLO;URSINI, ALDO
1997-01-01
Abstract
This paper deals with notions of (equational) definability of principal ideals in subtractive varieties. These notions are first characterized in several different ways. The strongest notion (EDPI) is then further investigated. We introduce the variety of MINI algebras (a generalization of Hilbert algebras) and we show that they are a paradigm for subtractive EDPI varieties. Finally we deal with principal ideal operations, and in particular with the cases of meet and join of principal ideals being equationally definable.
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https://hdl.handle.net/11365/1014175