Injective

English

An injective mapping

Etymology

Template:Rfe This term was introduced by Template:W in his treatise Éléments de mathématique.

Pronunciation

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Adjective

1. Template:Lb 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

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2. Template:Lb Loosely, having a certain generalizing property, abstracted from the study of $\mathbb{Q}$ as a $\mathbb{Z}$-module. Formally, such that any short exact sequence of (left) $R$-modules beginning with $M$ splits, or any of several equivalent statements: See Template:W.
3. Template:Lb Loosely, having a property analogous to that which characterizes injective 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 Template:W.
4. Template:Lb Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).

Related terms

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Translations

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See also

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French

Pronunciation

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Adjective

1. Template:Feminine singular of