McCoy property of Hurwitz series rings

Abstract

Based on a theorem of McCoy on commutative rings, Nielsen called a ring [Formula: see text] right McCoy if for any nonzero polynomials [Formula: see text] over [Formula: see text], [Formula: see text] implies [Formula: see text] for some [Formula: see text]. In this note, we introduce and investigate McCoy and [Formula: see text]-properties of Hurwitz series ring [Formula: see text] and its Hurwitz polynomial subring [Formula: see text]. We show that when [Formula: see text] is a reversible or duo ring and [Formula: see text] then the Hurwitz polynomial ring [Formula: see text] is McCoy.