Finite affine algebras are fully dualizable. Issue 4 (3rd April 2018)

• Record Type: Journal Article
• Authors: Bentz, Wolfram; Gillibert, Pierre; Sequeira, Luís
• Is Part Of: Communications in algebra. Volume 46:Issue 4(2018)
• Page Start: 1539
• Page End: 1553
• Publication Date: 2018-04-03
• Subjects: Abelian algebra -- affine algebra -- dualizable algebra -- natural duality -- strong duality; 08C20 -- 08B10; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1350693
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: We show that every finite affine algebra A admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structureA ∼ of finite type. We give an explicit bound on the arities of the partial and total operations appearing inA ∼ . In addition, we show that the enriched partial hom-clone of A is finitely generated as a clone.