Tagged Questions
5
votes
3answers
72 views
Proving a binary operation on $\mathbb{Z}$ gives a semigroup
Let $x\circ y= x +y-xy, \quad (x,y) \in \mathbb{Z}$
where $\circ$ is a binary operation on $\mathbb{Z}$, prove that this is a semigroup.
My Work
To prove we have to check two things:
$\mathbb{Z}$ ...
2
votes
2answers
97 views
hint request: counting the elements in a subset of a numerical semigroup
I'm working on a problem for an online judge and I'm stuck. I'd like a nudge in the right direction (not an outright solution, please), relevant references, theorems, etc. After reading through ...
6
votes
6answers
283 views
What are the subsemigroups of $(\mathbb N,+)?$
While trying to solve a somewhat bigger problem, I realized that I don't know what the subsemigroups of one of the most important semigroups, $(\mathbb N,+)$, are. (I assume $0\not\in\mathbb N$.) I've ...
