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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| 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 |
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doaj-35953df6d51a4768bf7824937ee8c2b92020-11-24T21:46:37ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252017-01-01201710.1155/2017/43491534349153A Topology on Milnor’s Group of a Topological Field and Continuous Joint DeterminantsSung Myung0Department of Mathematics Education, Inha University, 253 Yonghyun-dong, Nam-gu, Incheon 402-751, Republic of KoreaFor 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.http://dx.doi.org/10.1155/2017/4349153 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sung Myung |
| spellingShingle |
Sung Myung A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Sung Myung |
| author_sort |
Sung Myung |
| title |
A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants |
| title_short |
A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants |
| title_full |
A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants |
| title_fullStr |
A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants |
| title_full_unstemmed |
A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants |
| title_sort |
topology on milnor’s group of a topological field and continuous joint determinants |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2017-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2017/4349153 |
| work_keys_str_mv |
AT sungmyung atopologyonmilnorsgroupofatopologicalfieldandcontinuousjointdeterminants AT sungmyung topologyonmilnorsgroupofatopologicalfieldandcontinuousjointdeterminants |
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1725901056127270912 |