Central simple algebras

Louis Halle Rowen

doi:10.1007/BF02762016

Central simple algebras

Louis Halle Rowen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

Wedderburn's factorization of polynomials over division rings is refined and used to prove that every central division algebra of degree 8, with involution, has a maximal subfield which is a Galois extension of the center (with Galois group Z₂⊕Z₂⊕Z₂). The same proof, for an arbitrary central division algebra of degree 4, gives an explicit construction of a maximal subfield which is a Galois extension of the center, with Galois group Z₂⊕Z₂. Use is made of the generic division algebras, with and without involution.

Original language	English
Pages (from-to)	285-301
Number of pages	17
Journal	Israel Journal of Mathematics
Volume	29
Issue number	2-3
DOIs	https://doi.org/10.1007/BF02762016
State	Published - Jun 1978

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abstract = "Wedderburn's factorization of polynomials over division rings is refined and used to prove that every central division algebra of degree 8, with involution, has a maximal subfield which is a Galois extension of the center (with Galois group Z2⊕Z2⊕Z2). The same proof, for an arbitrary central division algebra of degree 4, gives an explicit construction of a maximal subfield which is a Galois extension of the center, with Galois group Z2⊕Z2. Use is made of the generic division algebras, with and without involution.",

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AB - Wedderburn's factorization of polynomials over division rings is refined and used to prove that every central division algebra of degree 8, with involution, has a maximal subfield which is a Galois extension of the center (with Galois group Z2⊕Z2⊕Z2). The same proof, for an arbitrary central division algebra of degree 4, gives an explicit construction of a maximal subfield which is a Galois extension of the center, with Galois group Z2⊕Z2. Use is made of the generic division algebras, with and without involution.

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Central simple algebras

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