Lecture notes on algebraic structure of lattice-ordered rings /:
Algebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field....
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, New Jersey :
World Scientific,
[2014]
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Algebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field. This book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-ordered rings to use as a self-study book. The book is largely self-contained, except in a few places, and contains about 200 exercises to assist the reader to better understand the text and practice some ideas. |
| Beschreibung: | 1 online resource (x, 247 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 241-243) and index. |
| ISBN: | 9789814571432 9814571431 |
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| 505 | 0 | |a Introduction to ordered algebraic systems. 1.1 Lattices. 1.2. Lattice-ordered groups and vector lattices. 1.3. Lattice-ordered rings and algebras -- 2. Lattice-ordered algebras with a d-basis. 2.1. Examples and basic properties. 2.2. Structure theorems -- 3. Positive derivations on l-rings. 3.1. Examples and basic properties. 3.2. f-ring and its generalizations. 3.3. Matrix l-rings. 3.4. Kernel of a positive derivation -- 4. Some topics on lattice-ordered rings. 4.1. Recognition of matrix l-rings with the entrywise order. 4.2. Positive cycles. 4.3. Nonzero f-elements in l-rings. 4.4. Quotient rings of lattice-ordered Ore domains. 4.5. Matrix l-algebras over totally ordered integral domains. 4.6. d-elements that are not positive. 4.7. Lattice-ordered triangular matrix algebras -- 5. l-ideals of l-unital lattice-ordered rings. 5.1. Maximal l-ideals. 5.2. l-ideals in commutative l-unital l-rings. | |
| 520 | |a Algebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field. This book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-ordered rings to use as a self-study book. The book is largely self-contained, except in a few places, and contains about 200 exercises to assist the reader to better understand the text and practice some ideas. | ||
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| contents | Introduction to ordered algebraic systems. 1.1 Lattices. 1.2. Lattice-ordered groups and vector lattices. 1.3. Lattice-ordered rings and algebras -- 2. Lattice-ordered algebras with a d-basis. 2.1. Examples and basic properties. 2.2. Structure theorems -- 3. Positive derivations on l-rings. 3.1. Examples and basic properties. 3.2. f-ring and its generalizations. 3.3. Matrix l-rings. 3.4. Kernel of a positive derivation -- 4. Some topics on lattice-ordered rings. 4.1. Recognition of matrix l-rings with the entrywise order. 4.2. Positive cycles. 4.3. Nonzero f-elements in l-rings. 4.4. Quotient rings of lattice-ordered Ore domains. 4.5. Matrix l-algebras over totally ordered integral domains. 4.6. d-elements that are not positive. 4.7. Lattice-ordered triangular matrix algebras -- 5. l-ideals of l-unital lattice-ordered rings. 5.1. Maximal l-ideals. 5.2. l-ideals in commutative l-unital l-rings. |
| ctrlnum | (OCoLC)875894451 |
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| dewey-raw | 511.3/3 |
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| spelling | Ma, Jingjing, author. http://id.loc.gov/authorities/names/n2013075710 Lecture notes on algebraic structure of lattice-ordered rings / Jingjing Ma, University of Houston-Clear Lake, USA. Hackensack, New Jersey : World Scientific, [2014] ©2014 1 online resource (x, 247 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 241-243) and index. Print version record. Introduction to ordered algebraic systems. 1.1 Lattices. 1.2. Lattice-ordered groups and vector lattices. 1.3. Lattice-ordered rings and algebras -- 2. Lattice-ordered algebras with a d-basis. 2.1. Examples and basic properties. 2.2. Structure theorems -- 3. Positive derivations on l-rings. 3.1. Examples and basic properties. 3.2. f-ring and its generalizations. 3.3. Matrix l-rings. 3.4. Kernel of a positive derivation -- 4. Some topics on lattice-ordered rings. 4.1. Recognition of matrix l-rings with the entrywise order. 4.2. Positive cycles. 4.3. Nonzero f-elements in l-rings. 4.4. Quotient rings of lattice-ordered Ore domains. 4.5. Matrix l-algebras over totally ordered integral domains. 4.6. d-elements that are not positive. 4.7. Lattice-ordered triangular matrix algebras -- 5. l-ideals of l-unital lattice-ordered rings. 5.1. Maximal l-ideals. 5.2. l-ideals in commutative l-unital l-rings. Algebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field. This book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-ordered rings to use as a self-study book. The book is largely self-contained, except in a few places, and contains about 200 exercises to assist the reader to better understand the text and practice some ideas. Lattice ordered rings. http://id.loc.gov/authorities/subjects/sh85074989 Algebra. http://id.loc.gov/authorities/subjects/sh85003425 Anneaux réticulés. Algèbre. algebra. aat MATHEMATICS General. bisacsh Algebra fast Lattice ordered rings fast has work: Lecture notes on algebraic structure of lattice-ordered rings (Text) https://id.oclc.org/worldcat/entity/E39PCH3cHWjHPGF7tkfYhJhQ4m https://id.oclc.org/worldcat/ontology/hasWork Print version: Ma, Jingjing. Lecture notes on algebraic structure of lattice-ordered rings 9789814571425 (DLC) 2013051147 (OCoLC)861671305 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=752589 Volltext |
| spellingShingle | Ma, Jingjing Lecture notes on algebraic structure of lattice-ordered rings / Introduction to ordered algebraic systems. 1.1 Lattices. 1.2. Lattice-ordered groups and vector lattices. 1.3. Lattice-ordered rings and algebras -- 2. Lattice-ordered algebras with a d-basis. 2.1. Examples and basic properties. 2.2. Structure theorems -- 3. Positive derivations on l-rings. 3.1. Examples and basic properties. 3.2. f-ring and its generalizations. 3.3. Matrix l-rings. 3.4. Kernel of a positive derivation -- 4. Some topics on lattice-ordered rings. 4.1. Recognition of matrix l-rings with the entrywise order. 4.2. Positive cycles. 4.3. Nonzero f-elements in l-rings. 4.4. Quotient rings of lattice-ordered Ore domains. 4.5. Matrix l-algebras over totally ordered integral domains. 4.6. d-elements that are not positive. 4.7. Lattice-ordered triangular matrix algebras -- 5. l-ideals of l-unital lattice-ordered rings. 5.1. Maximal l-ideals. 5.2. l-ideals in commutative l-unital l-rings. Lattice ordered rings. http://id.loc.gov/authorities/subjects/sh85074989 Algebra. http://id.loc.gov/authorities/subjects/sh85003425 Anneaux réticulés. Algèbre. algebra. aat MATHEMATICS General. bisacsh Algebra fast Lattice ordered rings fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85074989 http://id.loc.gov/authorities/subjects/sh85003425 |
| title | Lecture notes on algebraic structure of lattice-ordered rings / |
| title_auth | Lecture notes on algebraic structure of lattice-ordered rings / |
| title_exact_search | Lecture notes on algebraic structure of lattice-ordered rings / |
| title_full | Lecture notes on algebraic structure of lattice-ordered rings / Jingjing Ma, University of Houston-Clear Lake, USA. |
| title_fullStr | Lecture notes on algebraic structure of lattice-ordered rings / Jingjing Ma, University of Houston-Clear Lake, USA. |
| title_full_unstemmed | Lecture notes on algebraic structure of lattice-ordered rings / Jingjing Ma, University of Houston-Clear Lake, USA. |
| title_short | Lecture notes on algebraic structure of lattice-ordered rings / |
| title_sort | lecture notes on algebraic structure of lattice ordered rings |
| topic | Lattice ordered rings. http://id.loc.gov/authorities/subjects/sh85074989 Algebra. http://id.loc.gov/authorities/subjects/sh85003425 Anneaux réticulés. Algèbre. algebra. aat MATHEMATICS General. bisacsh Algebra fast Lattice ordered rings fast |
| topic_facet | Lattice ordered rings. Algebra. Anneaux réticulés. Algèbre. algebra. MATHEMATICS General. Algebra Lattice ordered rings |
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