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TRACE IDENTITIES OF FULL MATRIX ALGEBRAS OVER A FIELD OF CHARACTERISTIC ZERO
, 1974In this paper we consider the trace identities satisfied in a full matrix algebra of order n. For the case of a field of characteristic zero we prove that all trace identities are consequences of one obtained from the Hamilton-Cayley theorem.
Ju P Razmyslov
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ON THE CLASSIFICATION OF SIMPLE LIE ALGEBRAS OVER A FIELD OF NONZERO CHARACTERISTIC
, 1970We consider the question of the classification of simple finite-dimensional Lie algebras over an algebraically closed field K of characteristic p>3. It is well known that there exist examples of filtrations for which an associative graded Lie algebra has
V. Kac, G. M. Melikyan
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Multilinear identities of the Algebras over a Field of Characteristic P
International journal of algebra and computation, 1995We prove the theorem: Any associative PI-algebra over a field of characteristic p satisfies all the multilinear identities of the algebra of matrices of some finite order.
A. Kemer
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, 1988
Let be an algebraically closed field of characteristic , a universal Chevalley group over with an irreducible root system , a basis of , the set of radical weights that are nonnegative with respect to the natural ordering associated with , the set of ...
A. Premet
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Let be an algebraically closed field of characteristic , a universal Chevalley group over with an irreducible root system , a basis of , the set of radical weights that are nonnegative with respect to the natural ordering associated with , the set of ...
A. Premet
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, 2015
Fields and Matrix Algebra The Field Z3 The Field Axioms Field Examples Matrix Algebra over Different Fields Exercises Vector Spaces Definition of a Vector Space Vector Spaces of Functions Subspaces and More Examples of Vector Spaces Linear Independence ...
Hugo J. Woerdeman
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Fields and Matrix Algebra The Field Z3 The Field Axioms Field Examples Matrix Algebra over Different Fields Exercises Vector Spaces Definition of a Vector Space Vector Spaces of Functions Subspaces and More Examples of Vector Spaces Linear Independence ...
Hugo J. Woerdeman
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1967
In this Chapter, k will be an A-field; we use all the notations introduced for such fields in earlier Chapters, such as k A , k v , r v , etc. We shall be principally concerned with a simple algebra A over k; as stipulated in Chapter IX, it is always understood that A is central, i. e. that its center is k, and that it has a finite dimension over k; by
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In this Chapter, k will be an A-field; we use all the notations introduced for such fields in earlier Chapters, such as k A , k v , r v , etc. We shall be principally concerned with a simple algebra A over k; as stipulated in Chapter IX, it is always understood that A is central, i. e. that its center is k, and that it has a finite dimension over k; by
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On Matrix Algebras Over an Algebraically Closed Field [PDF]
The Annals of Mathematics, 1942 Recently a number of writers have discussed interesting developments in the theory of not completely reducible matrix sets and non-semisimple algebras.' Here we have made use of some of these concepts and methods to study matrix algebras over an algebraically closed field.
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1973
This chapter is a brief introduction into the structure of algebras, mostly finite dimensional, over any field k. The main contents are the Wedderburn theorems for a finite dimensional algebras A over an algebraically closed field k. If A has no nilpotent ideals ≠ 0, then A is a finite product of total matrix algebras over k. In this case, the set d (A)
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This chapter is a brief introduction into the structure of algebras, mostly finite dimensional, over any field k. The main contents are the Wedderburn theorems for a finite dimensional algebras A over an algebraically closed field k. If A has no nilpotent ideals ≠ 0, then A is a finite product of total matrix algebras over k. In this case, the set d (A)
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On some arithmetic properties of automorphic forms of GL(m) over a division algebra
, 2011In this paper we investigate arithmetic properties of automorphic forms on the group G' = GL_m/D, for a central division-algebra D over an arbitrary number field F.
H. Grobner, A. Raghuram
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Journal of Algebra and its Applications, 2017
Let [Formula: see text] be a finite-dimensional vector space over a field [Formula: see text] of characteristic zero, [Formula: see text] an anti-commutative product on [Formula: see text] and [Formula: see text] a bilinear form on [Formula: see text ...
J. Zhou, Liangyun Chen, Yao Ma, B. Sun
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Let [Formula: see text] be a finite-dimensional vector space over a field [Formula: see text] of characteristic zero, [Formula: see text] an anti-commutative product on [Formula: see text] and [Formula: see text] a bilinear form on [Formula: see text ...
J. Zhou, Liangyun Chen, Yao Ma, B. Sun
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