Tag Archives: transcendence degree

Commutative Algebra 42

Posted on April 30, 2020 by limsup

Noether Normalization Theorem Throughout this article, k is a field, not necessarily algebraically closed. Definition. Let A be a finitely generated k-algebra which is an integral domain. We say are algebraically independent over k if they are so as elements … Continue reading →

Posted in Advanced Algebra | Tagged , , , , , | 4 Comments

Commutative Algebra 41

Posted on April 29, 2020 by limsup

Basic Definitions The objective of this article is to establish the theory of transcendence bases for field extensions. Readers who are already familiar with this may skip the article. We will focus on field extensions here. Definition. Let be a … Continue reading →

Posted in Advanced Algebra | Tagged , , , | 2 Comments