ask a concept

liyi

In an exercise of my book, it defines "weak ring" (literally translated from Chinese) as follows.

$(R,+,\cdot)$ is a weak ring, if it satisfies:
(1) $(R,+)$ is an additive group; (it is abelian)
(2) $(R,\cdot)$ is a semigroup;
(3) There exist fixed elements $e_1,e_2$ such that
$x(y+z)=xy+xz-e_1$ and $(y+z)x=yx+zx-e_2$ for all $x,y,z\in R$ .

I cannot find such a name on internet...
Is it a special ring? Or just an exercise?

**Posted:** Wed Feb 09, 2005 1:23 am

Thomson

I think this might be called a semiring...here's a link:

http://mathworld.wolfram.com/Semiring.html

**Posted:** Fri Feb 18, 2005 1:22 am

liyi

It isn't. The distributivity is different.

**Posted:** Fri Feb 18, 2005 2:00 am