Definition of "nonassociative"

nonassociative

adjective
not comparable
1. Not associative.
2. (algebra, of an algebraic structure) Whose multiplication operation is not assumed to be associative for all elements.
  Quotations
  This book has been written about associative algebras. However, there is an analogous “PI-theory” that can be carried out for nonassociative rings, which is outlined here.
  1980, Lewis Halle Rowen, Polynomial Identities in Ring Theory, Academic Press, page 327
  Two important functions in nonassociative ring theory are the commutator and associator which, for elements a, b, c in a ring are defined respectively by [a, b] = ab − ba / and [a, b, c] = a(bc) − (ab)c.
  1996, E. G. Goodaire, E. Jespers, C. Polcino Milies, Alternative Loop Rings, Elsevier, page 5
  Authors in this book for the first time have constructed nonassociative structures like groupoids, quasi loops, non associative semirings and rings using finite complex modulo integers.
  2012, W. B. Vasantha Kandasamy, Florentin Smarandache, Non Associative Algebraic Structures Using Finite Complex Numbers, Zip Publishing, page 5