    Sentence 1: Under what condition is an element  irreducible? ;  Sentence 2:An element p-of R is called prime  element if it is neither zero nor a unit (Le. does  not have a 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 is irreducible if it is  Not a unit and cannot be written as a product of.  two ring elements that are not-units.