Sentence:  In the ring of integers, there are no <WSD>zero divisors</WSD> except 0. In a ring obtained from a Boolean algebra, on the other hand, every element except the identity is a <WSD>zero-divisor</WSD>. / The concept of a <WSD>zero-divisor</WSD> is intimately related to cancellation law as we see n the following proposition. / 1.7 Proposition: Let R be a ring and x\in R. Then for all y, x\in R, either of the equations xy=xz or yx=zx implies y=z if and only if x is not a <WSD>zero divisor</WSD>. In other words, cancellation by an element is possible iff it is not a <WSD>zero-divisor</WSD>. 
Meaning of the word marked with <WSD> tags:  An element "a" of a ring "R" for which there exists some nonzero element "x" ∈ "R" such that either "ax" = 0 or "xa" = 0.