Essential submodule
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
of a module $M$
A submodule $E$ of $M$ is essential it has a non-trival intersection with every non-trivial submodule of $M$: that is, $E \cap L = 0$ implies $L = 0$.
Dually, a submodule $S$ is superfluous if it is not a summand of $M$: that is, $S + L = M$ implies $L = M$.
See also: Essential subgroup.
References
- F.W. Anderson, K.R. Fuller, "Rings and Categories of Modules" Graduate Texts in Mathematics 13 Springer (2012) ISBN 1468499130
How to Cite This Entry:
Essential submodule. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Essential_submodule&oldid=54405
Essential submodule. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Essential_submodule&oldid=54405