1

On the wikipedia article about Quazigroups, there is a nice matrix chart of Group axioms and the structures that match a combination.

https://en.m.wikipedia.org/wiki/Quasigroup

Yet, i've noticed some combinations missing, they are:

  • only Identity
  • only Invertibility
  • Identity and Invertibility
  • Associativity and Invertibility
  • Totality and Identity

My question is - do such structures exist ? if yes - what are their names ?

p.s.: No mention of such primitive structures exists in related question Algebraic structure cheat sheet anyone?

and neither on larger wiki article: https://en.wikipedia.org/wiki/Outline_of_algebraic_structures

c69
  • 145
  • 2
    You cannot have invertibility without identity. The definition of the first requires the other. – freakish Jul 29 '18 at 09:11
  • ok - that should be "Magma with Identity" and such structure is called unital magma, per related question. https://math.stackexchange.com/q/2089449/18257 – c69 Jul 29 '18 at 18:00
  • @freakish - but Quazigroup has Totality + Invertibility without having Identity ? – c69 Jul 30 '18 at 03:34

0 Answers0