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Given a univariate polynomial  f ( x ) over a ring  R , we examine when we can write  f ( x ) as  g ( h ( x )), where  g  and  h  are polynomials of degree at least 2. We answer two questions of Gusić regarding when the existence of such  g  and  h  over an extension of  R  implies the existence of such  g  and  h  over  R .

TWO QUESTIONS ON POLYNOMIAL DECOMPOSITION