On associative spectra of operations

Abstract

The distance of an operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Associative spectra were introduced in a publication by B. Csákány and T. Waldhauser in 2000 for binary operations (see arXiv:1102.2124). We generalize this concept to p-ary operations, interpret associative spectra in terms of equational theories, and use this interpretation to find a characterization of fine spectra, to construct polynomial associative spectra, and to show that there are continuously many different spectra. Furthermore, an equivalent representation of bracketings is studied.

16 pages

Cited by in corpus (5)

• Associative spectra of graph algebras I. Foundations, undirected graphs, antiassociative graphs
• Associative spectra of graph algebras II. Satisfaction of bracketing identities, spectrum dichotomy
• Multiplication of matrices over lattices
• Norton algebras of the Hamming Graphs via linear characters
• The associative-commutative spectrum of a binary operation