• SOME CLASSES OF IRREDUCIBLE ELEMENTS IN FORMAL POWER SERIES RING OVER THE SET OF INTEGERS

Abstract

The formal power series ring is the natural extension of the polynomial ring over a certain ring R. If R is a field then the irreducible elements in R[[𝑥]] are of the form , where . Like ℤ[𝑥] and ℚ[𝑥] the irreducible elements in the formal power series ring over ℤ are still not completely determined. We will not discuss about the irreducible elements in ℤ[𝑥] or ℚ[𝑥] in this article. Here we shall discuss explicitly about some classes of irreducible elements in ℤ[[𝑥]]. We shall also give some theorems about the factorization in ℤ[[𝑥]].