nonassociative
English
Etymology
non- + associative
Adjective
nonassociative (not comparable)
- Not associative.
- (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.
- 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
- 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.
- 1980, Lewis Halle Rowen, Polynomial Identities in Ring Theory, Academic Press, page 327,
Further reading
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