On duality for skew field extensions

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this paper a duality principle is formulated for statements about skew field extensions of finite (left or right) degree. A proof for this duality principle is given by constructing for every extension L/K of finite degree a dual extension LJK, . These dual extensions are constructed by embedding a given L/K in an inner Galois extension N/K. The Appendix shows that such an embedding can always be constructed, and introduces the notion of an inner closure N for L/K.
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalJournal of algebra (Print)
Volume119
DOIs
Publication statusPublished - 1988

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Division ring or skew field
Field extension
Duality Principle
Duality
Galois Extension
Closure

Cite this

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title = "On duality for skew field extensions",
abstract = "In this paper a duality principle is formulated for statements about skew field extensions of finite (left or right) degree. A proof for this duality principle is given by constructing for every extension L/K of finite degree a dual extension LJK, . These dual extensions are constructed by embedding a given L/K in an inner Galois extension N/K. The Appendix shows that such an embedding can always be constructed, and introduces the notion of an inner closure N for L/K.",
author = "J. Treur",
year = "1988",
doi = "10.1016/0021-8693(88)90073-7",
language = "English",
volume = "119",
pages = "1--22",
journal = "Journal of algebra (Print)",
issn = "0021-8693",
publisher = "Academic Press Inc.",

}

On duality for skew field extensions. / Treur, J.

In: Journal of algebra (Print), Vol. 119, 1988, p. 1-22.

Research output: Contribution to JournalArticleAcademicpeer-review

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N2 - In this paper a duality principle is formulated for statements about skew field extensions of finite (left or right) degree. A proof for this duality principle is given by constructing for every extension L/K of finite degree a dual extension LJK, . These dual extensions are constructed by embedding a given L/K in an inner Galois extension N/K. The Appendix shows that such an embedding can always be constructed, and introduces the notion of an inner closure N for L/K.

AB - In this paper a duality principle is formulated for statements about skew field extensions of finite (left or right) degree. A proof for this duality principle is given by constructing for every extension L/K of finite degree a dual extension LJK, . These dual extensions are constructed by embedding a given L/K in an inner Galois extension N/K. The Appendix shows that such an embedding can always be constructed, and introduces the notion of an inner closure N for L/K.

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