English Explanatory Dictionary

injective

English dictionary entry

Meanings

adj
  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
  2. Loosely, having a certain generalizing property, abstracted from the study of ℚ as a ℤ-module. Formally, such that any short exact sequence of (left) R-modules beginning with M splits, or any of several equivalent statements: See Injective module.
  3. Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism f:X→Y in C, for every morphism g:X→Q there exists a morphism h:Y→Q such that h∘f=g; see Injective object.
  4. Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).

Pronunciation

/ɪnˈd͡ʒɛktɪv/ en-us-injective.ogg

Word forms

injective

Etymology

From French injectif

Synonyms

one-to-one

Related words

injectal bijective surjective

Derived words

injective cogenerator injective dimension injective function injective hull injectively injective map injective module injectiveness injective object injective patch injective sheaf injectivity noninjective selfinjective
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