On Commutativity and Groupoid Identities between Products with 3 Factors

Tjark Weber. International Journal of Algebra, 3(5):199-210, 2009.

Abstract

A groupoid consists of a set G equipped with a binary operation. This article examines the relationship between commutativity and various (less common) groupoid identities between products with 3 factors, e.g., (xy)z = (yz)x. We systematically study all 12 identities of this form to identify additional conditions (e.g., unitality) that are sufficient for commutativity. Automated deduction techniques were used in several parts of the work.

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BibTeX

@article{weber09commutativity,
  author  = {Tjark Weber},
  title   = {On Commutativity and Groupoid Identities between Products with 3 Factors},
  journal = {International Journal of Algebra},
  volume  = {3},
  number  = {5},
  pages   = {199--210},
  year    = {2009}
}