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Left Ideal


In a noncommutative ring R, a left ideal is a subset I which is an additive subgroup of R and such that for all r in R and all a in I,

 ra in I.

A left ideal of R can be characterized as a right ideal of the opposite ring of R.

In a commutative ring, the notions of right ideal and left ideal coincide.


See also

Ideal, One-Sided Ideal, Two-Sided Ideal

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Left Ideal." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LeftIdeal.html

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