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A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants

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  • Sung Myung

Abstract

For the tuple set of commuting invertible matrices with coefficients in a given field, the joint determinants are defined as generalizations of the determinant map for the square matrices. We introduce a natural topology on Milnor’s -groups of a topological field as the quotient topology induced by the joint determinant map and investigate the existence of a nontrivial continuous joint determinant by utilizing this topology, generalizing the author’s previous results on the continuous joint determinants for the commuting invertible matrices over and .

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  • Sung Myung, 2017. "A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-5, December.
    • Handle: RePEc:hin:jijmms:4349153
    DOI: 10.1155/2017/4349153
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