Remarks on normal bases
Copyright policy )Remarks on normal bases
We prove that any Galois extension of commutative rings with normal basis and abelian Galois group of odd order has a self dual normal basis. Also we show that if S/R is an unramified extension of number rings with Galois group of odd order and $R$ is totally real then the normal basis does not exist for S/R.
- Department of Mathematics The University of Chicago United States
- University of Chicago United States
- University of Illinois System United States
- The University of Chicago United States
- University of Illinois at Urbana Champaign United States
Mathematics - Number Theory, cyclotomic extensions, FOS: Mathematics, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Number Theory (math.NT), normal bases, trace form
Mathematics - Number Theory, cyclotomic extensions, FOS: Mathematics, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Number Theory (math.NT), normal bases, trace form
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!