context: Prime numbers give rise to two more general concepts that apply to elements of any commutative ring R, an algebraic structure where addition, subtraction and multiplication are defined: prime elements and irreducible elements. An element p of R is called prime element if it is neither zero nor a unit (i.e., 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. In the ring Z of integers, the set of prime elements equals the set of irreducible elements, which is
question: ఒక ప్రధాన మూలకంగా పరిగణించటానికి R యొక్క మూలకం p తప్పక సంతృప్తి చెందాల్సిన ఒక షరతు ఏమిటి?
answers: it is neither zero nor a unit neither zero nor a unit it is neither zero nor a unit it is neither zero nor a unit