perfect field
perfect field noun: a field K such that every irreducible polynomial over K has distinct roots.
Noun
perfect field (plural perfect fields)
- A field K such that every irreducible polynomial over K has distinct roots.
- If K is a perfect field of prime characteristic p, and if n is a nonnegative integer, then the mapping α→α from K to K is an automorphism.1984, Julio R. Bastida, Field Extensions and Galois Theory, Cambridge University Press, Addison-Wesley, page 10
- So far this stronger conjecture has been proved by Nazarova and Roiter over algebraically closed fields, and subsequently by Ringel over perfect fields.2001, Tsit-Yuen Lam, A First Course in Noncommutative Rings, 2nd edition, Springer, page 116
perfect field meaning in Tamil
perfect field in Tamil
- செவ்விய களம்
Forms of perfect field
| plural | perfect fields |
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Questions about perfect field
- What does perfect field mean?
- Perfect field means a field K such that every irreducible polynomial over K has distinct roots.
- What is perfect field in Tamil?
- Perfect field in Tamil is செவ்விய களம். See Perfect field meaning in Tamil.
- What part of speech is perfect field?
- Perfect field is a noun.
- What is the plural of perfect field?
- The plural of perfect field is perfect fields.
Words near perfect field in the dictionary
Source and license
Adapted from Wiktionary: perfect field (page history and authors); perfect field (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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