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seems sufficiently important that it ought to be mentioned again in the body of the article, and perhaps even elaborated on with a proof and some examples. The ring of algebraic integers of a number field is such a ring, and these are widely
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Maximal ideals are important because the quotients of rings by maximal ideals are simple rings, and in the special case of unital commutative rings they are also fields.
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It's not isomorphic. The quotient 2Z/4Z is the two-element non-unital ring where addition is modulo two, but multiplication is constantly zero.—
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Is not a unital ring the same as a ring with multiplicative identity? If so, why using two names for the same thing?Please edit
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Corrected that every maximal ideal is prime to include the fact that the ring must be commutative.
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I just noticed this comment of mine after starting a new maximal ideal article with material from
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Knowledge. If you would like to participate, please visit the project page, where you can join
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seem to be overlapping and are confusing. Citation needed? Or some more comments. (
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the quotient of a commutative ring with unit, by a maximal ideal, is a field
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Is it true that 2Z/4Z is not a field? It seems that it is isomorphic to Z
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The quotient of a unital commutative ring by a maximal ideal is a field
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I redirected this page and merged the old content into
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