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Simple Subrings of Algebras Over Fields [PDF]
Proceedings of the American Mathematical Society, 1981 In this note we shall prove that if A is a not necessarily associative algebra over a field K and S is a simple subring of A with centroid F then dim/r R < dimjf A. Since we do not use polynomial identities in a proof of this result then we have obtained an affirmative answer to the 11th question from (2), posed by I. N. Herstein.
Jan Krempa
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Algebraic complexities and algebraic curves over finite fields [PDF]
Journal of Complexity, 1987 We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180].
G. V. Chudnovsky, D. V. Chudnovsky
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Algebras over infinite fields [PDF]
Proceedings of the American Mathematical Society, 1956 A. S. Amitsur
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On the Triviality of Homogeneous Algebras over an Algebraically Closed Field [PDF]
Proceedings of the American Mathematical Society, 1975 Lowell Sweet
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Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4 [PDF]
, 2007 Except for blocks with a cyclic or Klein four defect group, it is not known in general whether the Morita equivalence class of a block algebra over a field of prime characteristic determines that of the corresponding block algebra over a p-adic ring.
Broué +6 more
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A Combinatorial Discussion on Finite Dimensional Leavitt Path Algebras [PDF]
, 2012 Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings.
Esin, Songul +7 more
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Noncommutative Geometry and Gauge Theory on Fuzzy Sphere [PDF]
, 2000 The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined.
Carow-Watamura, Ursula +1 more
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Almost Settling the Hardness of Noncommutative Determinant [PDF]
, 2011 In this paper, we study the complexity of computing the determinant of a matrix over a non-commutative algebra. In particular, we ask the question, "over which algebras, is the determinant easier to compute than the permanent?" Towards resolving this ...
Chien, Steve +3 more
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p-Algebras over an algebraic function field over a perfect field
Journal of Algebra, 1986 Verf. beweist folgenden Satz: Sei K ein algebraischer Funktionen-Körper in r Variablen über einem vollkommenen Körper. Jede p-Algebra A über K ist Brauer-äquivalent dem Kroneckerprodukt von r zyklischen Divisionsalgebren \(D_ i\) mit Exponent \(D_ i=Index D_ i\) und Exponent \(D_ i\leq Exponent A\). Für \(r=1\) ist das ein bekannter Satz von A.
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