Non-Commutative Valuation Rings and Semi-Hereditary Orders:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1997
|
| Series: | K-Monographs in Mathematics
3 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Much progress has been made during the last decade on the subjects of non commutative valuation rings, and of semi-hereditary and Prüfer orders in a simple Artinian ring which are considered, in a sense, as global theories of non-commutative valuation rings. So it is worth to present a survey of the subjects in a self-contained way, which is the purpose of this book. Historically non-commutative valuation rings of division rings were first treated systematically in Schilling's Book [Sc], which are nowadays called invariant valuation rings, though invariant valuation rings can be traced back to Hasse's work in [Has]. Since then, various attempts have been made to study the ideal theory of orders in finite dimensional algebras over fields and to describe the Brauer groups of fields by usage of "valuations", "places", "preplaces", "value functions" and "pseudoplaces". In 1984, N. 1. Dubrovin defined non-commutative valuation rings of simple Artinian rings with notion of places in the category of simple Artinian rings and obtained significant results on non-commutative valuation rings (named Dubrovin valuation rings after him) which signify that these rings may be the correct def inition of valuation rings of simple Artinian rings. Dubrovin valuation rings of central simple algebras over fields are, however, not necessarily to be integral over their centers |
| Physical Description: | 1 Online-Ressource (VIII, 192 p) |
| ISBN: | 9789401724364 9789048148530 |
| ISSN: | 1386-2804 |
| DOI: | 10.1007/978-94-017-2436-4 |
Staff View
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| 500 | |a Much progress has been made during the last decade on the subjects of non commutative valuation rings, and of semi-hereditary and Prüfer orders in a simple Artinian ring which are considered, in a sense, as global theories of non-commutative valuation rings. So it is worth to present a survey of the subjects in a self-contained way, which is the purpose of this book. Historically non-commutative valuation rings of division rings were first treated systematically in Schilling's Book [Sc], which are nowadays called invariant valuation rings, though invariant valuation rings can be traced back to Hasse's work in [Has]. Since then, various attempts have been made to study the ideal theory of orders in finite dimensional algebras over fields and to describe the Brauer groups of fields by usage of "valuations", "places", "preplaces", "value functions" and "pseudoplaces". In 1984, N. 1. Dubrovin defined non-commutative valuation rings of simple Artinian rings with notion of places in the category of simple Artinian rings and obtained significant results on non-commutative valuation rings (named Dubrovin valuation rings after him) which signify that these rings may be the correct def inition of valuation rings of simple Artinian rings. Dubrovin valuation rings of central simple algebras over fields are, however, not necessarily to be integral over their centers | ||
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| id | DE-604.BV042424289 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401724364 9789048148530 |
| issn | 1386-2804 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859706 |
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| physical | 1 Online-Ressource (VIII, 192 p) |
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| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer Netherlands |
| record_format | marc |
| series | K-Monographs in Mathematics |
| series2 | K-Monographs in Mathematics |
| spelling | Marubayashi, Hidetoshi Verfasser aut Non-Commutative Valuation Rings and Semi-Hereditary Orders by Hidetoshi Marubayashi, Haruo Miyamoto, Akira Ueda Dordrecht Springer Netherlands 1997 1 Online-Ressource (VIII, 192 p) txt rdacontent c rdamedia cr rdacarrier K-Monographs in Mathematics 3 1386-2804 Much progress has been made during the last decade on the subjects of non commutative valuation rings, and of semi-hereditary and Prüfer orders in a simple Artinian ring which are considered, in a sense, as global theories of non-commutative valuation rings. So it is worth to present a survey of the subjects in a self-contained way, which is the purpose of this book. Historically non-commutative valuation rings of division rings were first treated systematically in Schilling's Book [Sc], which are nowadays called invariant valuation rings, though invariant valuation rings can be traced back to Hasse's work in [Has]. Since then, various attempts have been made to study the ideal theory of orders in finite dimensional algebras over fields and to describe the Brauer groups of fields by usage of "valuations", "places", "preplaces", "value functions" and "pseudoplaces". In 1984, N. 1. Dubrovin defined non-commutative valuation rings of simple Artinian rings with notion of places in the category of simple Artinian rings and obtained significant results on non-commutative valuation rings (named Dubrovin valuation rings after him) which signify that these rings may be the correct def inition of valuation rings of simple Artinian rings. Dubrovin valuation rings of central simple algebras over fields are, however, not necessarily to be integral over their centers Mathematics Algebra Field theory (Physics) Associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Category Theory, Homological Algebra Commutative Rings and Algebras Field Theory and Polynomials Mathematik Miyamoto, Haruo Sonstige oth Ueda, Akira Sonstige oth K-Monographs in Mathematics 3 (DE-604)BV011222840 3 https://doi.org/10.1007/978-94-017-2436-4 Verlag Volltext |
| spellingShingle | Marubayashi, Hidetoshi Non-Commutative Valuation Rings and Semi-Hereditary Orders K-Monographs in Mathematics Mathematics Algebra Field theory (Physics) Associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Category Theory, Homological Algebra Commutative Rings and Algebras Field Theory and Polynomials Mathematik |
| title | Non-Commutative Valuation Rings and Semi-Hereditary Orders |
| title_auth | Non-Commutative Valuation Rings and Semi-Hereditary Orders |
| title_exact_search | Non-Commutative Valuation Rings and Semi-Hereditary Orders |
| title_full | Non-Commutative Valuation Rings and Semi-Hereditary Orders by Hidetoshi Marubayashi, Haruo Miyamoto, Akira Ueda |
| title_fullStr | Non-Commutative Valuation Rings and Semi-Hereditary Orders by Hidetoshi Marubayashi, Haruo Miyamoto, Akira Ueda |
| title_full_unstemmed | Non-Commutative Valuation Rings and Semi-Hereditary Orders by Hidetoshi Marubayashi, Haruo Miyamoto, Akira Ueda |
| title_short | Non-Commutative Valuation Rings and Semi-Hereditary Orders |
| title_sort | non commutative valuation rings and semi hereditary orders |
| topic | Mathematics Algebra Field theory (Physics) Associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Category Theory, Homological Algebra Commutative Rings and Algebras Field Theory and Polynomials Mathematik |
| topic_facet | Mathematics Algebra Field theory (Physics) Associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Category Theory, Homological Algebra Commutative Rings and Algebras Field Theory and Polynomials Mathematik |
| url | https://doi.org/10.1007/978-94-017-2436-4 |
| volume_link | (DE-604)BV011222840 |
| work_keys_str_mv | AT marubayashihidetoshi noncommutativevaluationringsandsemihereditaryorders AT miyamotoharuo noncommutativevaluationringsandsemihereditaryorders AT uedaakira noncommutativevaluationringsandsemihereditaryorders |