Meanings
- not comparableNot associative.
- not comparablealgebraWhose multiplication operation is not assumed to be associative for all elements.
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.
2 more examples
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 3272012, 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.
Synonyms & antonyms
adjectivenot associative
Synonym sets from Open English WordNet, CC BY 4.0.
Origin
Cite this entry
nonassociative. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/nonassociative
“nonassociative.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/nonassociative. Accessed November 3, 2026.
WatkinsX Dictionary, s.v. “nonassociative,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/nonassociative.
Source: nonassociative on Wiktionary, CC BY-SA 4.0.