cyclic algebra造句

• While working on his thesis, " Non-commutative polynomials and cyclic algebras ", he was advised by Joseph Wedderburn.
• Equivalently, any division algebra of period dividing " n " is Brauer equivalent to a tensor product of cyclic algebras of degree " n ".
• Even for a prime number " p ", there are examples showing that a division algebra of period " p " need not be actually isomorphic to a tensor product of cyclic algebras of degree " p ".
• Every class in the Brauer group is represented by a class in the Brauer group of an unramified extension of " L " / " K " of degree " n ", which by the Grunwald Wang theorem and the Albert Brauer Hasse Noether theorem we may take to be a cyclic algebra ( " L ", ?, ? " k " ) for some " k " mod " n ", where ? is the Frobenius map and ? is a uniformiser.