Sentence:  An element a of a ring is called a "zero-divisor" if a\ne 0 and ab = 0 or ba = 0 for some b\ne 0; if a is neither 0 nor a <WSD>zero-divisor</WSD>, it is said to be "regular" (see Section 7.1). A non-trivial ring without <WSD>zero-divisors</WSD> is called an "integral domain"; this term is not taken to imply commutativity. 
Meaning of the word marked with <WSD> tags:  A nonzero element "a" of a ring "R" for which there exists some nonzero element "x" ∈ "R" such that either "ax" = 0 or "xa" = 0.