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Dictionary

Words, grammatical forms and meanings linked to the ontology.

maximal ideal en · NOUN

Meanings

  1. (qualifier:ring theory) An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure).
    • Denote the minimal prime ideal in (b) by J#95;#92;mathsf#123;max#125;(#92;lambda), the unique maximal ideal of infinitesimal character #92;lambda. 1994, William M. McGovern, Completely Prime Maximal Ideals and Quantization, American Mathematical Society, page 15:
    • In particular, a prime ideal #92;mathfrak#123;p#125;#92;subsetA is a closed point of #92;mathrm#123;Spec#125;#92;A if and only if #92;mathfrak#123;p#125; is a maximal ideal. 2013, Igor R. Shafarevich, Basic Algebraic Geometry 2: Schemes and Complex Manifolds, 3rd edition, Springer, page 11:
    • 2004, Ayman Badawi, Abstract Algebra Manual: Problems and Solutions, Nova Science, 2nd Edition, page 87, Let S be the set of all prime ideals of B, and H be the set of all maximal ideals of B.

Forms

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maximal ideals Number=Plur lexicographic

Coordinates

minimal ideal

Relateds

maximal left ideal · maximal right ideal