We develop the theory of central ideals on commutative domains. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties. We provide a construction of the central seminormalization by a decomposition theorem in elementary central gluings. The existence of a central seminormalization is established in the affine case and for real schemes.
Cite this article
Jean-Philippe Monnier, Central algebraic geometry and seminormality. Rend. Sem. Mat. Univ. Padova 150 (2023), pp. 181–226DOI 10.4171/RSMUP/124