In mathematics, especially in the area of abstract algebra known as module theory, a ring R is called hereditary if all submodules of projective modules over R are again projective. If this is required only for finitely generated submodules, it is called semihereditary. For a noncommutative ring R, the terms left hereditary and left semihereditary and their right hand versions are used to distinguish the property on a single side of the ring. To be left (semi-)hereditary, all (finitely generated) submodules of projective left R-modules must be projective, and similarly to be right (semi-)hereditary all (finitely generated) submodules of projective right R-modules must be projective. It is possible for a ring to be left (semi-)hereditary but not right (semi-)hereditary and vice versa. (Wikipedia).
Definition of a Ring and Examples of Rings
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Ring and Examples of Rings - Definition of a Ring. - Definition of a commutative ring and a ring with identity. - Examples of Rings include: Z, Q, R, C under regular addition and multiplication The Ring of all n x
From playlist Abstract Algebra
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From playlist Abstract Algebra
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Stream Full Episodes of How It's Made: https://www.discoveryplus.com/show/how-its-made Subscribe to Science Channel: http://bit.ly/SubscribeScience Like us on Facebook: https://www.facebook.com/ScienceChannel Follow us on Twitter: https://twitter.com/ScienceChannel Follow us on Instag
From playlist How It's Made
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From playlist Abstract Algebra
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From playlist Abstract Algebra
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From playlist Abstract Algebra
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From playlist Abstract Algebra