A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants
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 K-groups of a topological field as the quotient topology induced by...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2017-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2017/4349153 |
| Summary: | 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 K-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 R and C. |
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| ISSN: | 0161-1712 1687-0425 |