essential submodule
Let be a submodule of a module .We say that is an essential submodule of ,and that is an essential extension of ,if whenever is a nonzero submodule of ,then is also nonzero.
A monomorphism is an essential monomorphismif the image is an essential submodule of .
Title | essential submodule |
Canonical name | EssentialSubmodule |
Date of creation | 2013-03-22 12:10:00 |
Last modified on | 2013-03-22 12:10:00 |
Owner | antizeus (11) |
Last modified by | antizeus (11) |
Numerical id | 6 |
Author | antizeus (11) |
Entry type | Definition |
Classification | msc 16D80 |
Synonym | essential extension |
Synonym | essential monomorphism |
Related topic | EssentialSubgroup |
Related topic | EssentialMonomorphisms |
Related topic | CompleteRingOfQuotientsOfReducedCommutativeRings |
Related topic | EpimorphicHull |