The New Encyclopædia BritannicaEncyclopædia Britannica, 1983 - Encyclopedias and dictionaries |
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Page 536
... field F contains as its smallest prime sub- field a copy of Z , for some prime p ( its characteristic ) , or of Q if of characteristic ∞ . FIELD EXTENSIONS Simple algebraic extensions . The preceding concepts make possible a far ...
... field F contains as its smallest prime sub- field a copy of Z , for some prime p ( its characteristic ) , or of Q if of characteristic ∞ . FIELD EXTENSIONS Simple algebraic extensions . The preceding concepts make possible a far ...
Page 539
... field extension obtained by successive adjunctions of roots a1 / n of constants a already constructed . It follows that if a polynomial equation p ( x ) = 0 over a field F can be solved by radicals , in the sense that its roots can be ...
... field extension obtained by successive adjunctions of roots a1 / n of constants a already constructed . It follows that if a polynomial equation p ( x ) = 0 over a field F can be solved by radicals , in the sense that its roots can be ...
Page 541
... field . The field extension con- struction to be described gives the real field R from the rational field Q ; the complex field C from the field Q ( V - 1 ) of all rational complex numbers r + sV = 1 ( r , s E Q ) ; and a new family of ...
... field . The field extension con- struction to be described gives the real field R from the rational field Q ; the complex field C from the field Q ( V - 1 ) of all rational complex numbers r + sV = 1 ( r , s E Q ) ; and a new family of ...
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