nonassociative

---

Adjective

nonassociative (not comparable)

1. Not associative.
2. (algebra, of an algebraic structure) Whose multiplication operation is not assumed to be associative for all elements.
   • 1980, Lewis Halle Rowen, Polynomial Identities in Ring Theory, Academic Press, page 327 ↗,

     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.

   • 1996, E. G. Goodaire, E. Jespers, C. Polcino Milies, Alternative Loop Rings, Elsevier, page 5 ↗,

     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.

   • 2012, W. B. Vasantha Kandasamy, Florentin Smarandache, Non Associative Algebraic Structures Using Finite Complex Numbers, Zip Publishing, 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.

---

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003