    Sentence 1: What is one condition that an element p of  R must satisfy in order to be considered a prime]  element?    Sentence 2: An element p of R is called prime element  if it is neither zero nor a unit (ie., does not have aj  multiplicative inverse) and satisfies the following}  requirement: given x and y in R such that p divides the}  product xy, then p divides x or y. An element ij  irreducible if it is not a unit and cannot be written as aj  product of two ring elements that are not units.