2
$\begingroup$

I'm looking for a name for the monoid given by the following table:

$ \begin{array}{c|ccc}&1&a&b\\ \hline 1&1&a&b\\ a&a&1&b\\ b&b&b&b \end{array} $

Is there a name that would be understandable to an undergraduate student who hasn't read anything about semigroups but has had a first course in algebra and knows what a semigroup/monoid is? What name would it be good to go under in a list of order-three semigroups?

  • 0
    @Asaf That's my grandfather's name. I'm not sure he'd be honored though.2012-07-02

2 Answers 2

7

Call it : $(\mathbb{Z}/3\mathbb{Z},*)$

  • 0
    it was the first think i saw :)2012-07-02
1

In computer science I would call it $\mathbb{Z}_2$ with errors, i.e. $ \langle \{0,1,\bot\},+,0\rangle $. In math I would follow hassan's idea.

  • 1
    @ymar Not zero, but an element that spreads like a virus (usually denoted by $\bot$). Any operation can result in an error $\bot$ (e.g. if you divide $1$ by $0$ in some algebra containing division) and if the "error result" is passed to any other expression, it propagates, i.e. the result of that expression has to be $\bot$ as well. Indeed, that kind of structures are denoted $G^\bot$, and called "$G$ with errors" or "$G$ with error handling". This is very similar to [NaNs](http://en.wikipedia.org/wiki/NaN) or monad `Maybe` from Haskell language (e.g. $G^\bot \cong \mathtt{Maybe}\ G$).2012-07-03