Sentence:  The set of natural numbers N with the usual operations of addition and multiplication is a <WSD>rig</WSD>, but not a ring. The set of integers Z is a ring. For a <WSD>rig</WSD>/ring (R,0,+,1,-), the set of polynomials R[x] on a generator x with the usual operations of addition and multiplication is also a <WSD>rig</WSD>/ring. 
Meaning of the word marked with <WSD> tags:  An algebraic structure similar to a ring, but without the requirement that every element have an additive inverse.