The Notion of Radical Ideals in MV-Algebras and Product MV-Algebras - Diaz Llano, Alejandro; Ramírez-Ramírez, Victor Hugo; Gonzalez, Jose Rodrigo (Statistics, Optimization & Information Computing, 2025)
In this work, we describe an interpretation of the radical of an ideal in the context of lu-groups, semi-low lu-rings and PMVf -algebras. These notions result naturally from a known notion in the context of MV-algebras and the use of categorical equivalences. The resulting notions in these contexts allow us to propose and prove a version of Hilbert’s Nullstellensatz Theorem.