Abstract algebra | Ideals (ring theory) | Ring theory

Minimal ideal

In the branch of abstract algebra known as ring theory, a minimal right ideal of a ring R is a nonzero right ideal which contains no other nonzero right ideal. Likewise, a minimal left ideal is a nonzero left ideal of R containing no other nonzero left ideals of R, and a minimal ideal of R is a nonzero ideal containing no other nonzero two-sided ideal of R . In other words, minimal right ideals are minimal elements of the poset of nonzero right ideals of R ordered by inclusion. The reader is cautioned that outside of this context, some posets of ideals may admit the zero ideal, and so the zero ideal could potentially be a minimal element in that poset. This is the case for the poset of prime ideals of a ring, which may include the zero ideal as a minimal prime ideal. (Wikipedia).

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In this video I talk about why minimalism is a thing people follow in today's society. There is a reason, and it's a good one.

From playlist Inspiration and Life Advice

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From playlist Real Numbers

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From playlist 241Fall13Ex3

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The Problem With Perfectionism

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From playlist SELF

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In this video I talk about why all mathematicians are actually minimalist, to some extent. Thoughts? Opinions? Leave a comment below:)

From playlist Cool Math Stuff

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We are – almost all of us – deeply attracted to the idea of being normal. But what if our idea of ‘normal’ isn’t normal? A plea for a broader definition of an important term. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/ojRR53 Join our mailing list: h

From playlist SELF

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Explosion and Minimal Logic

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From playlist Logic

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From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

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From playlist MAG

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From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

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From playlist CMSA Combinatorics Seminar

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From playlist An Introduction to the Arithmetic of Elliptic Curves

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From playlist Reel Ideas

Related pages

Prime ideal | Artinian ring | Duality (mathematics) | Simple ring | Abstract algebra | Socle (mathematics) | Minimal prime ideal | Division ring | Simple module | Domain (ring theory) | Maximal ideal | Kasch ring | Semiprime ring | Ring (mathematics) | Principal ideal | Ring theory