The Journal of the Indian Mathematical Society

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Division Algebras of Higher Degree over Rational Function Fields in One Variable


Affiliations
1 Department of Mathematics and Statistics University of Hyderabad, Gachibowli, Hyderabad - 500 046, India
     

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Let k be a field and ℓ a prime not equal to the characteristic of k. Assume that k contains a primitive ℓth ischolar_main of unity. Given a central simple algebra D over k(T) with ramification index at most 3, we show that there exist a centrals simple algebra D0 over k and f, g ∈ k(T)* such that D is Brauer equivalent to the tensor product of D0 and the cyclic algebra (f, g)ℓ over k(T). We also give necessary and sufficient conditions for the algebra D0⊗ (f, g)ℓ to be division for some class of polynomials f and g.

Keywords

Central Simple Algebras, Ramification Index, Rational Function Field.
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  • Division Algebras of Higher Degree over Rational Function Fields in One Variable

Abstract Views: 231  |  PDF Views: 0

Authors

Sudeep S. Parihar
Department of Mathematics and Statistics University of Hyderabad, Gachibowli, Hyderabad - 500 046, India
V. Suresh
Department of Mathematics and Statistics University of Hyderabad, Gachibowli, Hyderabad - 500 046, India

Abstract


Let k be a field and ℓ a prime not equal to the characteristic of k. Assume that k contains a primitive ℓth ischolar_main of unity. Given a central simple algebra D over k(T) with ramification index at most 3, we show that there exist a centrals simple algebra D0 over k and f, g ∈ k(T)* such that D is Brauer equivalent to the tensor product of D0 and the cyclic algebra (f, g)ℓ over k(T). We also give necessary and sufficient conditions for the algebra D0⊗ (f, g)ℓ to be division for some class of polynomials f and g.

Keywords


Central Simple Algebras, Ramification Index, Rational Function Field.

References