noether
Definition
Proper noun A German mathematician, Amalie Emmy Noether (1882–1935), renowned for her groundbreaking contributions to abstract algebra and theoretical physics. Her work fundamentally transformed these fields.
Examples of Usage
- Proper noun:
- Emmy Noether formulated a profound theorem linking symmetries in physics to conservation laws.
- The concept of a Noetherian ring is a central idea in modern algebra, named in her honor.
- Many consider Noether to be one of the most important mathematicians of the 20th century.
Advanced Usage
- "Noether's Theorem": A fundamental theorem in theoretical physics and calculus of variations, stating that every differentiable symmetry of the action of a physical system corresponds to a conservation law.
- Noether's theorem elegantly connects the symmetry of time translation to the conservation of energy.
- "Noetherian" (adjective): Pertaining to a mathematical structure (like a ring or module) that satisfies the ascending chain condition, a key concept in abstract algebra named after her.
- The proof relies on the ring being Noetherian.
Variants and Related Words
- Noetherian (adj): Describing a certain type of algebraic structure with a finiteness condition, as in "Noetherian ring" or "Noetherian module."
- Noetherian ring (n): A ring in which every ascending chain of ideals eventually stabilizes.
Synonyms
- Emmy Noether (full name)
- Amalie Emmy Noether (full name)
Related Phrases
- Noetherian induction: A method of mathematical proof applicable in Noetherian structures.
- Noether normalization lemma: A key result in commutative algebra.
Noun
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German mathematician (1882-1935)
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