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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2017/4349153 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562458810646528 |
|---|---|
| author | Sung Myung |
| author_facet | Sung Myung |
| author_sort | Sung Myung |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-35953df6d51a4768bf7824937ee8c2b9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-35953df6d51a4768bf7824937ee8c2b92025-02-03T01:22:33ZengWileyInternational 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 |
| spellingShingle | Sung Myung A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2017/4349153 |
| work_keys_str_mv | AT sungmyung atopologyonmilnorsgroupofatopologicalfieldandcontinuousjointdeterminants AT sungmyung topologyonmilnorsgroupofatopologicalfieldandcontinuousjointdeterminants |