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" From geometry to quantum mechanics : "
Yoshiaki Maeda [and others], editors.
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BL
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| Record Number
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982390
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b736760
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| Title & Author
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Advances in ring theory /\ Dinh Van Huynh, Sergio R. López-Permouth, editors.
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| Publication Statement
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Basel ;New York :: Birkhäuser,, 2010.
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| Series Statement
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Trends in Mathematics
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| Page. NO
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1 online resource (vi, 345 pages) :: portraits
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| ISBN
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3034602863
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: 9783034602860
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3034602855
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9783034602853
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Cover13; -- Table of Contents13; -- Preface -- Applications of Cogalois Theory to Elementary Field Arithmetic -- 1. Introduction -- 2. Notation and terminology -- 3. What is Cogalois theory? -- 4. Basic concepts and results of Cogalois theory -- G-Radical extensions -- G-Kneser extensions -- The Kneser criterion -- Cogalois extensions -- Galois and Cogalois connections -- Strongly G-Kneser extensions -- G-Cogalois extensions -- 5. Examples of G-Cogalois extensions -- 6. Applications to elementary field arithmetic -- 6.1. Effective degree computation: -- 6.2. Exhibiting extension basis: -- 6.3. Finding all intermediate fields: -- 6.4. Primitive element: -- 6.5. When is a sum of radicals of positive rational numbers a rational number? -- 6.6. When can a positive algebraic number 945; be written as a finite sum of real numbers of type 177; n8730;i ai, 1<i <r? -- 6.7. When can a positive superposed radical not be decomposed into a finite sum of real numbers of type 177; n8730;i ai, 1<i <r? -- 6.8. When is a rational combination of powers from a given set of radicals of positive rational numbers itself a radical of a positive rational number? -- 6.9. Radical extensions of prime exponent: -- 6.10. Simple radical separable extensions having the USP: -- 7. Other applications -- 7.1. Binomial ideals and Grobner bases -- 7.2. Heckes systems of ideal numbers -- References -- On Big Lattices of Classes of R-modules Defined by Closure Properties -- 1. Introduction -- 1.1. The skeletons of R-tors, R-Serre and R-op -- 2. The big lattice R-sext -- 2.1. R-sext and R-nat -- 3. The big lattice R-qext -- 3.1. R-qext and R-conat -- 4. R-nat and R-conat -- 5. R-sext and R-qext -- References -- Reversible and Duo Group Rings -- 1. Introduction -- 2. Reversibility in group rings -- 2.1. Reversibility in group algebras KG -- 2.2. Reversible group rings over commutative rings -- 2.3. Minimal reversible group rings -- 3. Duo group rings -- 3.1. Duo group algebras -- 3.2. Duo group rings over integral domains -- 4. Graded reversibility in integral group rings -- References -- Principally Quasi-Baer Ring Hulls -- References -- Strongly Prime Ideals of Near-rings of Continuous Functions -- 1. Preliminaries -- 2. Strongly prime ideals in N0(Rn) -- 3. Strongly prime ideals in N0(R969;) -- References -- Elements of Minimal Prime Ideals in General Rings -- Introduction -- 1. On r-strongly prime ideals -- 2. Weak zero-divisors -- 3. Examples and special rings -- References -- On a Theorem of Camps and Dicks -- 1. The theorem -- References -- Applications of the Stone Duality in the Theory of Precompact Boolean Rings -- 1. Preliminaries -- 2. Topologies on a Boolean ring -- 3. Countably linearly compact Boolean rings -- 4. On minimal topologies -- 5. Intersection of totally bounded topologies -- 6. The Bohr topology on a Boolean ring -- 7. Compact topologies on Boolean rings -- 8. Dense ideals of a ring -- 9. Self-injective Boolean rings -- 10. Zero-dimensional F-spaces -- 11. Necessary conditions for countably compactness -- 12. Basically disconnected spaces -- 13. Open questions -- References -- Over Rings and Functors -- Introduction -- 1. Preliminaries -- 2. Large right ideals -- 3. Mod-R and mod-Q for R 8834; Q.
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| Abstract
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This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra.
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| Subject
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Rings (Algebra)
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MATHEMATICS-- Algebra-- Intermediate.
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Rings (Algebra)
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| Dewey Classification
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512/.4
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| LC Classification
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QA247.A38 2010
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| Added Entry
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Huynh, Dinh Van,1947-
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López-Permouth, S. R., (Sergio R.),1957-
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