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单词 EssentialSubmodule
释义

essential submodule


Let X be a submoduleMathworldPlanetmath of a module Y.We say that X is an essential submodule of Y,and that Y is an essential extension of X,if whenever A is a nonzero submodule of Y,then AX is also nonzero.

A monomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath f:XY is an essential monomorphismif the image imf is an essential submodule of Y.

Titleessential submodule
Canonical nameEssentialSubmodule
Date of creation2013-03-22 12:10:00
Last modified on2013-03-22 12:10:00
Ownerantizeus (11)
Last modified byantizeus (11)
Numerical id6
Authorantizeus (11)
Entry typeDefinition
Classificationmsc 16D80
Synonymessential extension
Synonymessential monomorphism
Related topicEssentialSubgroup
Related topicEssentialMonomorphisms
Related topicCompleteRingOfQuotientsOfReducedCommutativeRings
Related topicEpimorphicHull
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