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injective MATH

Einsprachige Beispiele (nicht von der PONS Redaktion geprüft)

Englisch
If a ring is injective over itself as a right module, then it is called a right self-injective ring.
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The map between these quotient groups is either an isomorphism or is injective and has an image of index 2.
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The converse is a result of: if every module has a unique maximal injective submodule, then the ring is hereditary.
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When the domain manifold is compact, the notion of a smooth embedding is equivalent to that of an injective immersion.
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Given a finite-dimensional module over a commutative ring, the pairing may be injective (hence nondegenerate in the above sense) but not unimodular.
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The category of abelian sheaves has enough injective objects: this means that any sheaf is a subsheaf of an injective sheaf.
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There is an analogous definition using injective resolutions and cochain complexes.
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The function "f" itself need not be injective, only its derivative.
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In the dual point of view, an injective map corresponds to a surjection of sheaves, and a surjective map corresponds to an injection of sheaves.
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In fact, injective sheaves are flabby ("flasque"), soft, and acyclic.
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