An Introduction to Nonassociative Algebras by Richard D. Schafer
About this book :-
This little book is an expanded version of the lectures on nonassociative algebras which author has gave at an Advanced Subject Matter Institute in Algebra, which was held at Oklahoma State University in the summer of 1961 under the sponsorship of the National Science Foundation. This concise study was the first book to bring together material on the theory of nonassociative algebras, which had previously been scattered throughout the literature. It emphasizes algebras that are, for the most part, finite-dimensional over a field. After an introductory chapter, the book explores arbitrary nonassociative algebras and alternative algebras. Subsequent chapters concentrate on Jordan algebras and power-associative algebras. Throughout, an effort has been made to present the basic ideas, techniques, and flavor of what happens when the associative law is not assumed. Many of the proofs are given in complete detail.
Concise study presents in a short space some of the important ideas and results in the theory of nonassociative algebras, with particular emphasis on alternative and (commutative) Jordan algebras. Written as an introduction for graduate students and other mathematicians meeting the subject for the first time, the treatment's prerequisites include an acquaintance with the fundamentals of abstract and linear algebra.
After an introductory chapter, the book explores arbitrary nonassociative algebras and alternative algebras. Subsequent chapters concentrate on Jordan algebras and power-associative algebras. Throughout, an effort has been made to present the basic ideas, techniques, and flavor of what happens when the associative law is not assumed. Many of the proofs are given in complete detail.
Book Detail :-
Title:
An Introduction to Nonassociative Algebras by Richard D. Schafer
Publisher:
Project Gutenberg
Year:
2008
Pages:
81
Type:
PDF
Language:
English
ISBN-10 #:
0486688135
ISBN-13 #:
978-0486688138
License:
Linked content owned by author
Amazon:
Amazon
About Author :-
The author
Richard D. Schafer
(1918–2014) was an American mathematician and Professor of Mathematics at the Massachusetts Institute of Technology from 1959 until his retirement in 1988. His wife Alice Turner Schafer (1915–2009) was also a mathematician. Schafer did research on algebra, specifically on Jordan algebras and Lie algebras. He is best known for his textbook An Introduction to Nonassociative Algebras, first published in 1966, which has been freely available since 2008 from Project Gutenberg. He also studied the Cayley–Dickson construction. He received his PhD from the University of Chicago under Abraham Adrian Albert with dissertation Alternative Algebras over an Arbitrary Field in 1942. After service in the U.S. Naval Reserve from 1942 to 1945, he was an instructor at the University of Michigan for the academic year 1945–1946. From 1946 to 1948 he was at the Institute for Advanced Study. From 1948 to 1953 he was a professor at the University of Pennsylvania. From 1953 to 1958 he was at University of Connecticut as professor and head of the mathematics department. He spent the academic year 1958–1959 at the Institute for Advanced Study. From 1959 until his retirement in 1988, he was a professor at the Massachusetts Institute of Technology. In 2012 he was elected was a Fellow of the American Mathematical Society.
Book Contents :-
1. Introduction
2. Arbitrary Nonassociatlve Algebras
3. Alternative Algebras
4. Jordan Algebras
5. Power-Associative Algebras
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