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Mathematical Treasure: Peirce’s Linear Associative Algebra (1882)

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

Benjamin Peirce (1809-1880) was an American mathematician and a pioneering researcher in the field of algebras. His Linear Associative Algebra (1882) was originally published in lithograph form in 1870, then as a lengthy article in the American Journal of Mathematics (Issue 4, pp. 97-215) in 1881. His notion of “linear” is not the one used in modern “linear” algebra.

Title page of Linear Associative Algebra (1882) by Benjamin Peirce

In the beginning of his work, Peirce provided definitions of the concepts he would be working with. The first few pages present some then new terms to mathematical vocabulary, including “idempotent” and “nilpotent.”

Page 11 of Linear Associative Algebra (1882) by Benjamin Peirce

Page 12 of Linear Associative Algebra (1882) by Benjamin Peirce

Page 13 of Linear Associative Algebra (1882) by Benjamin Peirce

Page 14 of Linear Associative Algebra (1882) by Benjamin Peirce

The images above were obtained through the courtesy of the University of California Libraries. The book may be viewed in its entirety in the Internet Archive.

Index to Mathematical Treasures 

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Peirce’s Linear Associative Algebra (1882)," Convergence (January 2018)

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