10 Noetherian and Artinian Laurent rings

Kapitel in diesem Buch

1. Frontmatter I
2. Contents VII
3. Introduction IX
4. 1 Preliminary properties of A((x, φ)) and M((x, φ)) 1
5. 2 Noetherian rings A((x, φ)) 10
6. 3 Serial and Bezout rings A((x, φ)) 17
7. 4 Prime and semiprime skew Laurent series rings 31
8. 5 Regular and biregular Laurent series rings 39
9. 6 Equivalent definitions of Laurent rings 47
10. 7 Generalized Laurent rings 53
11. 8 Properties of Laurent rings 63
12. 9 Laurent rings: examples, relation 67
13. 10 Noetherian and Artinian Laurent rings 81
14. 11 Simple and semisimple Laurent rings 87
15. 12 Uniserial and serial Laurent rings 91
16. 13 Semilocal Laurent rings 98
17. 14 Filtrations and (generalized) Malcev–Neumann rings 106
18. 15 Properties of generalized Malcev–Neumann rings 113
19. 16 Properties and examples of Malcev–Neumann rings 118
20. 17 Laurent series in two variables 126
21. Bibliography 129
22. Notation 133
23. Index 135