Márki / Wiegandt Theory of Radicals

1. Auflage 2014
ISBN: 978-1-4832-9644-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 310 Seiten, Web PDF

Reihe: Colloquia Mathematica Societatis Janos Bolyai

Radicals arose originally from structural investigations in rings, but later on they infiltrated into various branches of algebra, as well as into topology and relational structures. This volume is the result of a conference attended by mathematicians from all five continents and thus represents the current state of research in the area.

Autoren/Hrsg.

Márki, L.

Wiegandt, R.

Inhaltsverzeichnis

1;Front Cover;1
2;Theory of Radicals;2
3;Copyright Page;3
4;Table of Contents;4
5;Preface;6
6;Schedule for talks;8
7;List of Participants;12
8;Chapter 1. On Essential Extensions, Maximal Essential Extensions and Iterated Maximal Essential Extensions in Radical Theory;18
8.1;1. Essential covers, intersection property and special radicals;18
8.2;2. Maximal essential extension and atoms of the lattice of all radicals;21
8.3;3. Iterated maximal essential extension;23
8.4;References;26
9;Chapter 2. A Structure Theorem for O-Groups;28
9.1;1. Introduction;28
9.2;2. Prime ideals and subdirect products;29
9.3;3. Examples;31
9.4;References;34
10;Chapter 3. Quasi-division Rings — Some Examples of Quasiregular Rings;36
10.1;ABSTRACT;36
10.2;1. Introduction;36
10.3;2. Construction of some classes of quasi-division rings;38
10.4;3. Examples;44
10.5;4. Some properties of Fas a ring;50
10.6;Acknowledgement;59
10.7;References;59
11;Chapter 4. Strongly Hereditary Strict Radicals and Quotient Categories of Commutative Rings;62
11.1;1. The quotient category defined by the prime radical;64
11.2;2. No localizing subcategories, again;72
11.3;3. A postscripton non-abelian localizing subcategories;75
11.4;References;75
12;Chaptre 5. Radicals in Abelian Groups;78
12.1;Introduction;78
12.2;1. Basic facts about radicals;80
12.3;2. The cardinal condition;82
12.4;3. Radicals commuting with certain products;92
12.5;4. Torsion theories;100
12.6;5. Constructing groups from radicals;102
12.7;References;105
13;Chapter 6. Radicals of Graded Rings;110
13.1;1. Introduction;110
13.2;2. Notations and terminology;111
13.3;3. Group graded rings;115
13.4;4. Rings graded by unique product semigroups;120
13.5;5. Rings graded by inverse semigroups;123
13.6;6. Semilattice Graded Rings;125
13.7;References;127
14;Chapter 7. A General Approach to the Structure of Radicals in Some Ring Constructions;132
14.1;1. Main definition;132
14.2;2. Radicals restorable by idempotents;134
14.3;3. Radicals restorable by subgroups;137
14.4;4. Radicals restorable by the Archimedean components of a commutative semigroup;139
14.5;5. Applications and connections with other results;139
14.6;References;143
15;Chapter 8. Closed Ideals in Non-Unital Morita Rings;146
15.1;1. Introduction;146
15.2;2. Lattice-isomorphisms of u.c. (I.e.) ideals;147
15.3;3. Applications of u.c. (I.c.) ideals;151
15.4;Acknowledgement;155
15.5;References;155
16;Chapter 9. Radical Extensions;158
16.1;1. Introduction;158
16.2;2. Class functions;159
16.3;3. Some applications;164
16.4;4. The dual theory;169
16.5;References;173
17;Chapter 10. The Distributive Radical;176
17.1;1. Introduction;176
17.2;2. The distributive radical of modules;177
17.3;3. The distributive radical of rings;179
17.4;4. Properties of the distributive radical of rings;183
17.5;References;185
18;Chapter 11. Radical Ideals of Radically Simple Rings and their Extensions;186
18.1;Introduction;186
18.2;1. Radically simple rings;186
18.3;2. AS–rings;189
18.4;3. Polynomial rings;192
18.5;References;196
19;Chapter 12. Classes of Strongly Semiprime Rings;198
19.1;ABSTRACT;198
19.2;1. Introduction;198
19.3;2. .-classes;203
19.4;3. Semi-superprime rings;205
19.5;4. Semi-uniformly strongly prime rings;207
19.6;References;209
20;Chapter 13. Some Questions Concerning Radicals of Associative Rings;210
20.1;1. Lattices of radicals;211
20.2;2. Radicals of rings with an additional structure;218
20.3;References;226
21;Chapter 14. Some Remarks about Modularity of Lattices of Radicals of Associative Rings;230
21.1;References;238
22;Chapter 15. Some Subidempotent Radicals;240
22.1;References;249
23;Chapter 16. The Radical of Locally Compact Alternative and Jordan Rings;250
23.1;1. Introduction;250
23.2;2. The connected component;251
23.3;3. Local structure of locally compact rings;255
23.4;4. The radical of a Q-ring;259
23.5;References;262
24;Chapter 17. On Non-Hypersolvable Radicals of Not Necessarily Associative Rings;264
24.1;1. c-radicals;265
24.2;2. Semisimplicity of free rings;271
24.3;References;274
25;Chapter 18. To the Abstract Theory of Radicals: A Contribution from Near-Rings;276
25.1;1. Introduction;276
25.2;2. Preliminaries;277
25.3;3. Radicals and ideals;280
25.4;4. Overnilpotent radicals;288
25.5;5. Some open problems;293
25.6;References;295
26;Chapter 19. Complementary Radical Classes of Proper Semifields;298
26.1;ABSTRACT;298
26.2;1. Preliminaries on the radical theory of proper semifields;298
26.3;2. R-classes and S-classes;302
26.4;3. Non-trivial complementary radical classes;305
26.5;References;310