As a sequel to [2] and [15] we investigate ideal properties focusing on subtractive varieties. Here we probe the relations between congruences and ideals in subtractive varieties, in order to give some means to recover the congruence structure from the ideal structure. To do so we consider mainly two operators from the ideal lattice to the congruence lattice of a given algebra and we classify subtractive varieties according to various properties of these operators. In the last section several examples are discussed in details.
Agliano', P., Ursini, A. (1997). On subtractive varieties III: from ideals to congruences. ALGEBRA UNIVERSALIS, 37(3), 296-333 [10.1007/s000120050020].
On subtractive varieties III: from ideals to congruences
AGLIANO', PAOLO;URSINI, ALDO
1997-01-01
Abstract
As a sequel to [2] and [15] we investigate ideal properties focusing on subtractive varieties. Here we probe the relations between congruences and ideals in subtractive varieties, in order to give some means to recover the congruence structure from the ideal structure. To do so we consider mainly two operators from the ideal lattice to the congruence lattice of a given algebra and we classify subtractive varieties according to various properties of these operators. In the last section several examples are discussed in details.
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https://hdl.handle.net/11365/17588