Race condition
A race condition or race hazard is the behavior of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events. It becomes a bug when one or more of the possible behaviors is undesirable.
Ore condition
The Ore condition can be generalized to other multiplicative subsets, and is presented in textbook form in and . A subset "S" of a ring "R" is called a right denominator set if it satisfies the following three conditions for every "a", "b" in "R", and "s", "t" in "S":
If "S" is a right denominator set, then one can construct the ring of right fractions "RS" similarly to the commutative case. If "S" is taken to be the set of regular elements (those elements "a" in "R" such that if "b" in "R" is nonzero, then "ab" and "ba" are nonzero), then the right Ore condition is simply the requirement that "S" be a right denominator set.