Live briefing
Everything about Noether normalization lemma
Result of commutative algebra
In mathematics, the Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether in 1926. It states that for any field, and any finitely generated commutative k-algebra, there exist elements in that are algebraically independent over and such that is a finitely generated module over the polynomial ring. The integer is equal to the Krull dimension of the ring ; and if is an integral domain, is also the transcendence degree of the field of fractions of over k. Wikipedia →
đź§ Start here: a 6-step reading path
- Read the overview: Noether normalization lemmaA 5-minute orientation
- Read the landmark paper: A Differential Analog of the Noether Normalization LemmaCited 2 times
- Go sideways: Verma moduleA closely related topic
- Go sideways: Integral elementA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
📚 Books worth reading
Open Library didn't respond; try again in a moment.
đź”— Related topics
- Verma module Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. Verma modules can be used…
- Integral element In commutative algebra, an element b of a commutative ring B is said to be integral over a subring A of B if b is a root of some monic polynomial over…
- Dimension theory (algebra) In mathematics, dimension theory is the study in terms of commutative algebra of the notion of dimension of an algebraic variety (and by extension that…
- Glossary of Lie groups and Lie algebras This is a glossary for the terminology applied in the mathematical theories of Lie groups and Lie algebras. For the topics in the representation theory…
- Valuation ring In abstract algebra, a valuation ring is an integral domain D such that for every non-zero element x of its field of fractions F, at least one of x or…
- Spectrum of a ring In mathematics, and more specifically in commutative algebra and algebraic geometry, the prime spectrum (or simply the spectrum) of a commutative ring…
- Weight (representation theory) In the mathematical field of representation theory, the concept of weights of an algebra A over a field F is a generalisation of that of eigenvalues. They…
- Lie coalgebra In mathematics a Lie coalgebra is the dual structure to a Lie algebra. In finite dimensions, these are dual objects: the dual vector space to a Lie algebra…