Commutative algebra | Ring theory

Jacobson ring

In algebra, a Hilbert ring or a Jacobson ring is a ring such that every prime ideal is an intersection of primitive ideals. For commutative rings primitive ideals are the same as maximal ideals so in this case a Jacobson ring is one in which every prime ideal is an intersection of maximal ideals. Jacobson rings were introduced independently by Wolfgang Krull , who named them after Nathan Jacobson because of their relation to Jacobson radicals, and by Oscar Goldman, who named them Hilbert rings after David Hilbert because of their relation to Hilbert's Nullstellensatz. (Wikipedia).

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Ring Definition (expanded) - Abstract Algebra

A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a rin

From playlist Abstract Algebra

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The Jacobs Ladder-o-Phone of Fire!

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levitron

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Jacobs Ladder Toy Variations

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From playlist Abstract Algebra

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From playlist Course on Rings and Modules (Abstract Algebra 4) [Graduate Course]

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From playlist Virtual Conference

Related pages

Prime ideal | Hilbert's Nullstellensatz | Jacobson radical | David Hilbert | Nilradical of a ring | Krull dimension | Maximal ideal | Algebraic geometry | Zariski's lemma | Primitive ideal