irreducible element
non-zero non-unit element in an integral domain that is not a product of two non-units
prime element
nonzero, non-unit element p in a commutative ring R such that, whenever p divides ab for some a and b in R, then p divides a or p divides b (or both)
irreducible polynomial
irreducible element in the ring of polynomials; a non-constant polynomial that is not the product of two non-constant polynomials