1
$\begingroup$

Let the element $x$ of a commutative semigroup has the property $x=a+b\Rightarrow a=x~$or $b=x$. I call such an element "prime". My question is: what is the right term about such elements.

p.s. I am not an algebraist.

$\endgroup$

1 Answer 1

2
$\begingroup$

The right term should rather be irreducible and the definition should be slightly different:
$x$ is irreducible if $x = \sum_{i \in I} x_i$, then there exists $i \in I$ such that $x = x_i$. The subtle difference with your definition is that if your semigroup has a neutral element $0$ (think of $\mathbb{N}$), then $0 = \sum_{i \in \emptyset} x_i$ and hence $0$ is not irreducible.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .