Anodality (also termed u-closedness) is a notion coming from K-theory and is usefull when studying Pic A[X, X-1]. An injective ring morphismA→Bis called anodal if an elementxinBbelongs toAwheneverThen a ringAwith total quotient ringKis said to be anodal ifA→Kis anodal. We show that a weak Baer ringAis anodal if and only if for each pair (a, b) ∈ A2such thatthere is some z ∈Asuch that. Anodality of weak Baer rings is descended by faithfully flat or anodal morphisms. We defineu-integral morphisms similar toR. Swan's subintegral morphisms and show that for any injective morphismA→Bthere is a u-closuresuch thatis u-integral. A u-integral morphism is locally an epimorphism and is a direct limit of unramified morphisms. This result has many consequences. An injective integral morphism which is injective on the spectrum is locally anodal whence anodal. If A is a weak Baer ring, then A is locally anodal if A is locally unibranched; the converse is true if, in addition, A is one-dimensional and Noetherian. We introduce new closures for injective ring morphismsA→Bin order to evaluate. In some measure, seminormality and anodality are dual notions : among other results, we get that Picfis injective for a u-integral ring morphismf, while Picfis surjective iffis subintegral.