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On the Numbers Field Q (v), where v2p + P2 (v + 1) = 0

✍ Scribed by Lorraine L. T. Foster

Publisher: John Wiley and Sons
Year: 1970
Tongue: English
Weight: 230 KB
Volume: 44
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19700440111

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✦ Synopsis

In ARTIS [I] examples of cubic algebraic number fields & ( a ) are treated i l l which the index o f v is not one, and hence (1, v, vz} is not an integral bitsis. It would seem that in the literature there are few examples of fields & ( I ) ) of higher degree in which the index of 7) is not one. This paper arose as a conseqiience of a search for such examples which would be of interest to students of my a.lgebraic iiumber theory class and which would serve a h suita.ble illustrations of the theory. The quartic field Q ( v ) where v C + 4 u + 1 = 0 was found to provide such an example. Indeed, it follows rather immediately that, v3j2 is an integer, a'nd in fact, a unit. Hence it seeined of interest to generalize and study the equation x X p + p ? ( x + I ) = 0,

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