Meaning of maximal ideal | Babel Free

Definitions

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).

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.”

“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.”

“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.”

CEFR level