Lecture notes on algebraic structure of lattice-ordered rings:
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hackensack, New Jersey
World Scientific
[2014]
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| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Description based on print version record |
| Physical Description: | 1 online resource (x, 247 pages) illustrations |
| ISBN: | 9789814571432 9814571431 |
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MARC
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| 505 | 8 | |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 | |
| 505 | 8 | |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 | |
| 650 | 7 | |a MATHEMATICS / General |2 bisacsh | |
| 650 | 4 | |a Lattice ordered rings | |
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Record in the Search Index
| _version_ | 1804175386397900800 |
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| any_adam_object | |
| author | Ma, Jingjing |
| author_facet | Ma, Jingjing |
| author_role | aut |
| author_sort | Ma, Jingjing |
| author_variant | j m jm |
| building | Verbundindex |
| bvnumber | BV043030497 |
| classification_rvk | SK 230 |
| collection | ZDB-4-EBA |
| 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 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 |
| ctrlnum | (OCoLC)875894451 (DE-599)BVBBV043030497 |
| dewey-full | 511.3/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/3 |
| dewey-search | 511.3/3 |
| dewey-sort | 3511.3 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043030497 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:15:28Z |
| institution | BVB |
| isbn | 9789814571432 9814571431 |
| language | English |
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| oclc_num | 875894451 |
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| physical | 1 online resource (x, 247 pages) illustrations |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Ma, Jingjing Verfasser aut 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 txt rdacontent c rdamedia cr rdacarrier Description based on 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 MATHEMATICS / General bisacsh Lattice ordered rings Algebra Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf Algebraischer Ring (DE-588)4141855-4 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 s Algebraischer Ring (DE-588)4141855-4 s 1\p DE-604 Erscheint auch als Druck-Ausgabe Ma, Jingjing Lecture notes on algebraic structure of lattice-ordered rings Erscheint auch als Druckausgabe 978-981-4571-42-5 Erscheint auch als Druckausgabe 981-4571-42-3 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=752589 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 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 MATHEMATICS / General bisacsh Lattice ordered rings Algebra Algebraische Struktur (DE-588)4001166-5 gnd Algebraischer Ring (DE-588)4141855-4 gnd |
| subject_GND | (DE-588)4001166-5 (DE-588)4141855-4 |
| 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 | MATHEMATICS / General bisacsh Lattice ordered rings Algebra Algebraische Struktur (DE-588)4001166-5 gnd Algebraischer Ring (DE-588)4141855-4 gnd |
| topic_facet | MATHEMATICS / General Lattice ordered rings Algebra Algebraische Struktur Algebraischer Ring |
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| work_keys_str_mv | AT majingjing lecturenotesonalgebraicstructureoflatticeorderedrings |