# a "ring" whose addition lacks inverses, terminology

• July 22nd 2011, 03:06 PM
ymar
a "ring" whose addition lacks inverses, terminology
Is there a name for an algrebraic structure with two operations, addition and multiplication, such that

1) the additive structure is that of a commutative monoid;
2) the multiplicative structue is that of a monoid;

A simple example would be any power set with the operations $\cup$ and $\cap$, but also the set of all binary relations on a set with the operations $\cup$ and $\circ$, the latter being the composition of relations.
• July 22nd 2011, 04:48 PM
NonCommAlg
Re: a "ring" whose addition lacks inverses, terminology
the name is semiring.
• July 23rd 2011, 03:50 AM
ymar
Re: a "ring" whose addition lacks inverses, terminology
Thanks. I checked "quasi-" and "pseudo-", but forgot "semi-". :-)
• July 23rd 2011, 03:54 AM
Swlabr
Re: a "ring" whose addition lacks inverses, terminology
Quote:

Originally Posted by ymar
Is there a name for an algrebraic structure with two operations, addition and multiplication, such that

1) the additive structure is that of a commutative monoid;
2) the multiplicative structue is that of a monoid;
A simple example would be any power set with the operations $\cup$ and $\cap$, but also the set of all binary relations on a set with the operations $\cup$ and $\circ$, the latter being the composition of relations.