Laurent Series Rings and Related Rings
Description
In this book, ring-theoretical properties of skew Laurent series rings A (( x; f )) over a ring A , where A is an associative ring with non-zero identity element are described. In addition, we consider Laurent rings and Malcev-Neumann rings, which are proper extensions of skew Laurent series rings.
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Person
Askar Tuganbaev , National Research University MPEI, Lomonosov Moscow State University, Russia.
Content
- Intro
- Contents
- Introduction
- 1 Preliminary properties of A((x, f)) and M((x, f))
- 2 Noetherian rings A((x, f))
- 3 Serial and Bezout rings A((x, f))
- 4 Prime and semiprime skew Laurent series rings
- 5 Regular and biregular Laurent series rings
- 6 Equivalent definitions of Laurent rings
- 7 Generalized Laurent rings
- 8 Properties of Laurent rings
- 9 Laurent rings: examples, relation
- 10 Noetherian and Artinian Laurent rings
- 11 Simple and semisimple Laurent rings
- 12 Uniserial and serial Laurent rings
- 13 Semilocal Laurent rings
- 14 Filtrations and (generalized) Malcev-Neumann rings
- 15 Properties of generalized Malcev-Neumann rings
- 16 Properties and examples of Malcev-Neumann rings
- 17 Laurent series in two variables
- Bibliography
- Notation
- Index
