Laurent Series Rings and Related Rings

Askar Tuganbaev

Published by De Gruyter 2020

Laurent Series Rings and Related Rings

Askar Tuganbaev

https://doi.org/10.1515/9783110702248

Overview
Contents

About this book

In this book, ring-theoretical properties of skew Laurent series rings A((x; φ)) 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.

In-depth study on Laurent ring series.
Written by well-known expert in the field.

Author information

Askar Tuganbaev, National Research University MPEI, Lomonosov Moscow State University, Russia.

Topics

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

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in mathematics.
Pages
- Front matter: 14
- Main content: 136
Illustrations
- Illustrations: 10
Keywords: Laurent series.

eBook

Published: September 21, 2020
ISBN: 9783110702248

Hardcover

Published: September 21, 2020
ISBN: 9783110702163