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International Journal of Mathematics and Mathematical Sciences
Volume 2017 (2017), Article ID 4349153, 5 pages
https://doi.org/10.1155/2017/4349153
Research Article

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

Department of Mathematics Education, Inha University, 253 Yonghyun-dong, Nam-gu, Incheon 402-751, Republic of Korea

Correspondence should be addressed to Sung Myung; rk.ca.ahni@1gnuym-s

Received 28 September 2017; Accepted 26 November 2017; Published 12 December 2017

Academic Editor: Daniel Simson

Copyright © 2017 Sung Myung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 .