Laurent series rings and related rings / Askar Tuganbaev.

Format:

Book

Author/Creator:

Tuganbaev, Askar A., author.

Language:

English

Subjects (All):

Rings (Algebra).

Physical Description:

1 online resource (XIV, 136 p.)

Place of Publication:

Berlin ; Boston : De Gruyter, [2020]

Language Note:

In English.

Summary:

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.

Contents:

Frontmatter

Contents

Introduction

1 Preliminary properties of A((x, φ)) and M((x, φ))

2 Noetherian rings A((x, φ))

3 Serial and Bezout rings A((x, φ))

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

Notes:

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9783110702248

311070224X

OCLC:

1198929282