by Au Yun-Nam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 133-137). / Introduction --- p.iv / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- Some Semigroup Properties --- p.1 / Chapter 1.2 --- General Properties of Semigroup Algebras --- p.5 / Chapter 1.3 --- Group Algebras --- p.7 / Chapter 1.3.1 --- Some Basic Properties of Groups --- p.7 / Chapter 1.3.2 --- General Properties of Group Algebras --- p.8 / Chapter 1.3.3 --- Δ-Method for Group Algebras --- p.10 / Chapter 1.4 --- Graded Algebras --- p.12 / Chapter 1.5 --- Crossed Products and Smash Products --- p.14 / Chapter 2 --- Radicals of Graded Rings --- p.17 / Chapter 2.1 --- Jacobson Radical of Crossed Products --- p.17 / Chapter 2.2 --- Graded Radicals and Reflected Radicals --- p.18 / Chapter 2.3 --- Radicals of Group-graded Rings --- p.24 / Chapter 2.4 --- Algebras Graded by Semilattices --- p.26 / Chapter 2.5 --- Algebras Graded by Bands --- p.27 / Chapter 2.5.1 --- Hereditary Radicals of Band-graded Rings --- p.27 / Chapter 2.5.2 --- Special Band-graded Rings --- p.30 / Chapter 3 --- Radicals of Semigroup Algebras --- p.34 / Chapter 3.1 --- Radicals of Polynomial Rings --- p.34 / Chapter 3.2 --- Radicals of Commutative Semigroup Algebras --- p.36 / Chapter 3.2.1 --- Commutative Cancellative Semigroups --- p.37 / Chapter 3.2.2 --- General Commutative Semigroups --- p.39 / Chapter 3.2.3 --- The Nilness and Semiprimitivity of Commutative Semigroup Algebras --- p.45 / Chapter 3.3 --- Radicals of Cancellative Semigroup Algebras --- p.48 / Chapter 3.3.1 --- Group of Fractions of Cancellative Semigroups --- p.48 / Chapter 3.3.2 --- Jacobson Radical of Cancellative Semigroup Algebras --- p.54 / Chapter 3.3.3 --- Subsemigroups of Polycyclic-by-Finite Groups --- p.57 / Chapter 3.3.4 --- Nilpotent Semigroups --- p.59 / Chapter 3.4 --- Radicals of Algebras of Matrix type --- p.62 / Chapter 3.4.1 --- Properties of Rees Algebras --- p.62 / Chapter 3.4.2 --- Algebras Graded by Elementary Rees Matrix Semigroups --- p.65 / Chapter 3.5 --- Radicals of Inverse Semigroup Algebras --- p.68 / Chapter 3.5.1 --- Properties of Inverse Semigroup Algebras --- p.69 / Chapter 3.5.2 --- Radical of Algebras of Clifford Semigroups --- p.72 / Chapter 3.5.3 --- Semiprimitivity Problems of Inverse Semigroup Algebras --- p.73 / Chapter 3.6 --- Other Semigroup Algebras --- p.76 / Chapter 3.6.1 --- Completely Regular Semigroup Algebras --- p.76 / Chapter 3.6.2 --- Separative Semigroup Algebras --- p.77 / Chapter 3.7 --- Radicals of Pi-semigroup Algebras --- p.80 / Chapter 3.7.1 --- PI-Algebras --- p.80 / Chapter 3.7.2 --- Permutational Property and Algebras of Permutative Semigroups --- p.80 / Chapter 3.7.3 --- Radicals of PI-algebras --- p.82 / Chapter 4 --- Finiteness Conditions on Semigroup Algebras --- p.85 / Chapter 4.1 --- Introduction --- p.85 / Chapter 4.1.1 --- Preliminaries --- p.85 / Chapter 4.1.2 --- Semilattice Graded Rings --- p.86 / Chapter 4.1.3 --- Group Graded Rings --- p.88 / Chapter 4.1.4 --- Groupoid Graded Rings --- p.89 / Chapter 4.1.5 --- Semigroup Graded PI-Algebras --- p.91 / Chapter 4.1.6 --- Application to Semigroup Algebras --- p.92 / Chapter 4.2 --- Semiprime and Goldie Rings --- p.92 / Chapter 4.3 --- Noetherian Semigroup Algebras --- p.99 / Chapter 4.4 --- Descending Chain Conditions --- p.107 / Chapter 4.4.1 --- Artinian Semigroup Graded Rings --- p.107 / Chapter 4.4.2 --- Semilocal Semigroup Algebras --- p.109 / Chapter 5 --- Dimensions and Second Layer Condition on Semigroup Algebras --- p.119 / Chapter 5.1 --- Dimensions --- p.119 / Chapter 5.1.1 --- Gelfand-Kirillov Dimension --- p.119 / Chapter 5.1.2 --- Classical Krull and Krull Dimensions --- p.121 / Chapter 5.2 --- The Growth and the Rank of Semigroups --- p.123 / Chapter 5.3 --- Dimensions on Semigroup Algebras --- p.124 / Chapter 5.4 --- Second Layer Condition --- p.128 / Notations and Abbreviations --- p.132 / Bibliography --- p.133
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_321534 |
| Date | January 1996 |
| Contributors | Au, Yun-Nam., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, vii, 133 leaves ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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