  We develop the theory of central ideals on commutative rings. 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.
