Characterizations of Endomorphic Nuclei on R0-Algebras (Nilpotent Minimum Algebras)
Hongjun Zhou and Bin Zhao
In the present paper, the Glivenko theorem is extended to nilpotent minimum algebras (NM-algebras, for short) with a nucleus, which provides several necessary and sufficient conditions for the underlying nucleus to be an endomorphism. A particularly interesting characterization shows that a nucleus on an NM-algebra is an endomorphism if it is a double relative negation defined by an element whose (canonical) negation is a fixpoint of the t-norm square operation.
Keywords: Non-classical logics; nilpotent minimum algebra; R0-algebra; Glivenko theorem; nucleus; relative negation.