Techreport,
On associative spectra of operations
Preprint, MATH-AL-02-2008. TU Dresden, Institut für Algebra, (2008)
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. We generalize this concept to $2 p$-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.
