injective

injective englanniksi

1. Of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic

(syn)

2. Loosely, having a certain generalizing property, abstracted from the study of \mathbb{Q} as a \mathbb{Z}-module. Formally, such that any exact sequence of (left) R-modules beginning with M splits, or any of several equivalent statements: See (w).

3. Loosely, having a property analogous to that which characterizes projective modules (see above). Formally, such that, given a monomorphism f:X \to Y in C, for every morphism g:X \to Q there exists a morphism h: Y \to Q such that h \circ f = g; see (w).

4. Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).

5. (feminine singular of)