The Notion of Radical Ideals in MV-Algebras and Product MV-Algebras
Keywords:
Radical, Nullstellensatz, MV-algebras, Product MV-algebras, lattice-ordered groups, lattice-ordered rings
Abstract
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.
Published
2025-08-12
How to Cite
Gonzalez, J. R., Diaz Llano, A., & Ramírez-Ramírez, V. H. (2025). The Notion of Radical Ideals in MV-Algebras and Product MV-Algebras. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2479
Issue
Section
Research Articles
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
