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essential extension Essential ideal essential submodule superfluous submodule

EN

In mathematics, specifically module theory, given a ring R and an R-module M with a submodule N, the module M is said to be an essential extension of N if for every submodule H of M, H ∩ N = { 0 } {\displaystyle H\cap N=\{0\}\,} implies that H = { 0 } {\displaystyle H=\{0\}\,} As a special case, an essential left ideal of R is a left ideal that is essential as a submodule of the left module RR.
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