On associative spectra of operations

Details On associative spectra of operations On associative spectra of operations

2011-02-11

arxiv.org/abs/1102.2337v1

Acta Sci. Math. (Szeged) 75 (2009) 433-456

Mathematics

Rings and Algebras

16 pages

Scientific paper

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.

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