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On Normal Bases for Finite Commutative Rings
Author(s) -
Steidl Gabriele
Publication year - 1990
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19901450112
Subject(s) - mathematics , polynomial ring , chinese remainder theorem , constructive , pure mathematics , commutative property , extension (predicate logic) , commutative ring , identity (music) , normal basis , finite field , galois module , polynomial , algebra over a field , discrete mathematics , mathematical analysis , process (computing) , physics , computer science , acoustics , programming language , operating system
This paper is devoted to the introduction of extension rings S : = R [ x ]/ gR [ x ] with a suitable polynomial g ϵ R [ x ] of arbitrary commutative rings R with identity and to the development of a normal basis concept of S over R , which is similar to that of Galois extensions of finite fields. We prove new results for Galois extensions of local rings and apply them together with the Chinese remainder theorem to solve the above task in a constructive way.