Totally t-closed rings Original Research Article

We define the class of totally t-closed rings: such rings are injective objects with respect to the class of infra-integral morphisms (injective integral ring morphisms with isomorphic residual extensions). Among other characterizations, we show that a ring is totally t-closed if and only if this ring is a t-closed Baer ring. We also obtain that for every reduced ring A, there exists a universal tight infra-integral morphism of A to a totally t-closed ring T(A), the so-called total t-closure of A. If one observes that a t-closed ring is seminormal, then T(A) can be seen as a construction analogous to the seminormalization. Moreover, several properties of totally t-closed rings are given.