maximal ideal

plural maximal ideals

1. ring theoryalgebraAn 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).

   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.

   2 more examples

   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