(2) The algebraic closure C of the complex number field c is C itself @ True. C is algebrai cally closed and contains @, and there can be no smaller algebraically closed field containing 6. ) True. Any field that contains IR and is algebrai cally closed must he equel to C. In particular, Ĉ = C. © False. the algeb Larger then K itself, so C is a proper subfield of C. O Filse. Because C is alveady olge braicelly closed itself, its ab- lic closure K of a field K is always strictly lic gebraic closure does not exist,

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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(2
The algebraic closure Ĉ of the complex number field C is C itself
@ True, C is algebrai cally closed and contains a, and there can
be no smaller algebraically closed field conteaiaing C.
) True, Any field that contuins IR and is algebrai caly clased
Must be equol to C. In parbicular, C = C.
False. The algebraic closure k of a field k is always scrictly
Larger then K itself, so C is a proper subfield of C.
O Fulse. Because C is alveady olgebraicelly elosed itself, ibs ab
gebraic closure does not exist,
Transcribed Image Text:(2 The algebraic closure Ĉ of the complex number field C is C itself @ True, C is algebrai cally closed and contains a, and there can be no smaller algebraically closed field conteaiaing C. ) True, Any field that contuins IR and is algebrai caly clased Must be equol to C. In parbicular, C = C. False. The algebraic closure k of a field k is always scrictly Larger then K itself, so C is a proper subfield of C. O Fulse. Because C is alveady olgebraicelly elosed itself, ibs ab gebraic closure does not exist,
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