# Ernst Schröder on Algebra and Logic The Four Inverse Operations

Ernst Schröder on Algebra and Logic : The Four Inverse Operations [English translation of the third chapter of Ernst Schröder’s Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende. Schröder discusses differences, quotients, roots, and logarithms and introduces techniques for manipulating equations involving these four inverse operations as well as the three direct ones. Venturing into the world of abstract algebra, he studies the behavior of a non-commutative form of multiplication with two inverses. Having allowed his operations to take classes as inputs and to have classes as outputs even when the inputs are individuals, he develops a powerful apparatus for handling this new class-algebra.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Ernst Schröder on Algebra and Logic The Four Inverse Operations

Part of the Synthese Library Book Series (volume 465)
Editors: Pollard, Stephen
62 pages

/lp/springer-journals/ernst-schro-der-on-algebra-and-logic-the-four-inverse-operations-t08NVp50oZ
Publisher
Springer International Publishing
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-031-05670-3
Pages
107 –169
DOI
10.1007/978-3-031-05671-0_3
Publisher site
See Chapter on Publisher Site

### Abstract

[English translation of the third chapter of Ernst Schröder’s Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende. Schröder discusses differences, quotients, roots, and logarithms and introduces techniques for manipulating equations involving these four inverse operations as well as the three direct ones. Venturing into the world of abstract algebra, he studies the behavior of a non-commutative form of multiplication with two inverses. Having allowed his operations to take classes as inputs and to have classes as outputs even when the inputs are individuals, he develops a powerful apparatus for handling this new class-algebra.]

Published: Apr 24, 2022