English

On associative spectra of operations

Rings and Algebras 2011-02-14 v1

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. Cs\'ak\'any 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.

Keywords

Cite

@article{arxiv.1102.2337,
  title  = {On associative spectra of operations},
  author = {Sebastian Liebscher and Tamás Waldhauser},
  journal= {arXiv preprint arXiv:1102.2337},
  year   = {2011}
}

Comments

16 pages

R2 v1 2026-06-21T17:24:55.607Z