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Simple algebras over local fields
1967Let D be a division algebra of finite dimension over any field K; we will consider left vector-spaces over D, whose dimension will always be assumed finite and
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Algebras with three anticommuting elements. II. Two algebras over a singular field
, 1981The Clifford algebra Ω generated by the elements {1,ω} with (ω)2 = +1, is an abelian ring of dimension two with properties analogous to the complex field C.
N. Salingaros, N. Salingaros
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, 2004
Recall i. Let L be a Lie algebra over a field F. An L-module V is a vector space over F together with a bilinear map L × V → V that sends the pair (l, v) ∈ L × V to an element denoted lv ∈ V such that [l, l′]v = l(l′v) − l′(lv) for all l, l′ ∈ L and v ...
Shlomo Sternberg
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Recall i. Let L be a Lie algebra over a field F. An L-module V is a vector space over F together with a bilinear map L × V → V that sends the pair (l, v) ∈ L × V to an element denoted lv ∈ V such that [l, l′]v = l(l′v) − l′(lv) for all l, l′ ∈ L and v ...
Shlomo Sternberg
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Some Remarks on Algebras Over an Algebraically Closed Field
The Annals of Mathematics, 1943The theory of rings with radicals is an interesting and far reaching problem of modern algebra.' In this paper we have examined some aspects of algebras which may have radicals and whose coefficient fields are algebraically closed. Some of the methods employed clearly could be used for less restricted algebras, but a full extension of the results ...
W. M. Scott, C. Nesbitt
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Groups of Algebras Over an Algebraic Number Field
American Journal of Mathematics, 1943Saunders MacLane, O. F. G. Schilling
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Cohomology of finite group schemes over a field
, 1997E. Friedlander, A. Suslin
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