Algebras.

Algebras, the last of the major algebraic objects in this book, are rings with a compatible vector space or module structure. Interest in algebras began with Hamilton's construction of the quaternions [1843] and Benjamin Peirce's paper Linear Associative Algebras [1864]. Algebras are fundamental to algebraic geometry and to the study of group representations (see Chapters VII and IX). [ABSTRACT FROM AUTHOR]