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- Essential_extension abstract "In mathematics, specifically module theory, given a ring R and R-modules M with a submodule N, the module M is said to be an essential extension of N (or N is said to be an essential submodule or large submodule of M) if for every submodule H of M,implies that As a special case, an essential left ideal of R is a left ideal which is essential as a submodule of the left module RR. The left ideal has non-zero intersection with any non-zero left ideal of R. Analogously, and essential right ideal is exactly an essential submodule of the right R module RRThe usual notations for essential extensions include the following two expressions:(Lam 1999), and (Anderson & Fuller 1992)The dual notion of an essential submodule is that of superfluous submodule (or small submodule). A submodule N is superfluous if for any other submodule H, implies that .The usual notations for superfluous submodules include:(Lam 1999), and (Anderson & Fuller 1992)".
- Essential_extension wikiPageID "10119238".
- Essential_extension wikiPageRevisionID "581622225".
- Essential_extension hasPhotoCollection Essential_extension.
- Essential_extension subject Category:Abstract_algebra.
- Essential_extension subject Category:Commutative_algebra.
- Essential_extension subject Category:Module_theory.
- Essential_extension comment "In mathematics, specifically module theory, given a ring R and R-modules M with a submodule N, the module M is said to be an essential extension of N (or N is said to be an essential submodule or large submodule of M) if for every submodule H of M,implies that As a special case, an essential left ideal of R is a left ideal which is essential as a submodule of the left module RR. The left ideal has non-zero intersection with any non-zero left ideal of R.".
- Essential_extension label "Essential extension".
- Essential_extension label "Wesentliche Erweiterung".
- Essential_extension sameAs Wesentliche_Erweiterung.
- Essential_extension sameAs m.02q2d5p.
- Essential_extension sameAs Q2563809.
- Essential_extension sameAs Q2563809.
- Essential_extension wasDerivedFrom Essential_extension?oldid=581622225.
- Essential_extension isPrimaryTopicOf Essential_extension.