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English[edit]
English Wikipedia has an article on:
Find 4,399 synonyms for transcendent and other similar words that you can use instead based on 14 separate contexts from our thesaurus. What's another word for What's the opposite of. The second turns to clinical practice and the importance of experience, transcendence, and temporality. In other words, the Chacoan road builders made a physical practice of transcendence, a word that comes from the Latin transcendere, to climb, step, or go across or over.
Wikipedia Noun[edit]
(pluraltranscendence degrees)
- (algebra, field theory, of a field extension) Given a field extensionL / K, the largest cardinality of an algebraically independentsubset of L over K.
- 2004, F. Hess, An Algorithm for Computing Isomorphisms of Algebraic Function Fields, Duncan Buell (editor), Algorithmic Number Theory: 6th International Symposium, ANTS-VI, LNCS 3076, page 263,
- Let and denote algebraic function fields of transcendence degree one.
- 2007, Anthony W. Knapp, Advanced Algebra, Springer (Birkhäuser), page 422,
- Lemma 7.19 Suppose that is a field extension[sic, meaning extension field] of transcendence degree over a field and that is not separably generated over . If are elements of such that , then for a suitable relabeling of the 's, the subfield of is of transcendence degree and is not separably generated over .
- 2008, Bernd Sturmfels, Algorithms in Invariant Theory, Springer, 2nd Edition, page 24,
- Proposition 2.1.1 Every finite matrix group has algebraically independent invariants, i.e., the ring has transcendence degree over .
- 2004, F. Hess, An Algorithm for Computing Isomorphisms of Algebraic Function Fields, Duncan Buell (editor), Algorithmic Number Theory: 6th International Symposium, ANTS-VI, LNCS 3076, page 263,
Usage notes[edit]
- A transcendence degree is said to be of a field extension (i.e., ). More properly, it is the cardinality of a particular type of subset of the extension field , although the context of the field extension is required to make sense of the definition.
- Relatedly, a transcendence basis of is a subset of that is algebraically independent over and such that is an algebraic extension of (that is, is an algebraic extension).
- It can be shown that every field extension has a transcendence basis, whose cardinality, denoted or , is exactly the transcendence degree of .
Synonyms[edit]
- (cardinality of largest algebraically independent subset of a given extension field):transcendental degree
Related terms[edit]
Translations[edit]
cardinality of largest algebraically independent subset of a given extension field
See also[edit]
Further reading[edit]
- Algebraic independence on Wikipedia.Wikipedia
- Algebraic independence on Encyclopedia of Mathematics
- Transcendence Degree on Wolfram MathWorld
Retrieved from 'https://en.wiktionary.org/w/index.php?title=transcendence_degree&oldid=51283562'
| transcendencein Spanish | in French | in Italian | English synonyms | English Usage | Conjugator | in context | images WordReference Random House Unabridged Dictionary of American English © 2020 tran•scend•encen. WordReference Random House Learner's Dictionary of American English © 2020
tran•scendv.[~ + object] WordReference Random House Unabridged Dictionary of American English © 2020
tran•scend•ent,adj.See -scend-. tran•scendv.t.
v.i.
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