Linear Associative Algebras - 1st Edition - ISBN: 9780080165646, 9781483186795

Linear Associative Algebras

1st Edition

Authors: Alexander Abian
eBook ISBN: 9781483186795
Imprint: Pergamon
Published Date: 1st January 1971
Page Count: 174
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Linear Associative Algebras focuses on finite dimensional linear associative algebras and the Wedderburn structure theorems.

The publication first elaborates on semigroups and groups, rings and fields, direct sum and tensor product of rings, and polynomial and matrix rings. The text then ponders on vector spaces, including finite dimensional vector spaces and matrix representation of vectors.

The book takes a look at linear associative algebras, as well as the idempotent and nilpotent elements of an algebra, ideals of an algebra, total matrix algebras and the canonical forms of matrices, matrix representation of algebras, and division of algebras. The manuscript also tackles the Wedderburn structure theorems, including direct sum and tensor product decomposition of algebras, nilpotent algebras and the radical of an algebra, and structure of simple and semi-simple algebras.

The publication is highly recommended for mathematicians and students interested in the Wedderburn structure theorems and finite dimensional linear associative algebras.

Table of Contents


1. Preliminaries

1.1. Semigroups and Groups

1.2. Rings and Fields

1.3. Direct Sum and Tensor Product of Rings

1.4. Polynomial Rings

1.5. Matrix Rings

2. Vector Spaces

2.1. Vector Spaces

2.2. Finite Dimensional Vector Spaces

2.3. Matrix Representation of Vectors

3. Linear Associative Algebras

3.1. Linear Associative Algebras

3.2. Idempotent and Nilpotent Elements of an Algebra

3.3. Ideals of an Algebra

3.4. Total Matrix Algebras and the Canonical Forms of Matrices

3.5. Matrix Representation of Algebras

3.6. Division Algebras

4. Wedderburn Structure Theorems

4.1. Direct Sum and Tensor Product Decomposition of Algebras

4.2. Nilpotent Algebras and the Radical of an Algebra

4.3. Structure of Semi-Simple Algebras

4.4. Structure of Simple Algebras

4.5. Concluding Remarks


Index of Symbols



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About the Author

Alexander Abian

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