Abstract

CHIMAL-DZUL, Henry  and  LOPEZ-ANDRADE, C. A.. When is R[x] a principal ideal ring?. Integración - UIS [online]. 2017, vol.35, n.2, pp.143-148. ISSN 0120-419X.  https://doi.org/10.18273/revint.v35n2-2017001.

Because of its interesting applications in coding theory, cryptography, and algebraic combinatorics, in recent decades a lot of attention has been paid to the algebraic structure of the ring of polynomials R[x], where R is a finite commutative ring with identity. Motivated by this popularity, in this paper we determine when R[x] is a principal ideal ring. In fact, we prove that R[x] is a principal ideal ring if and only if R is a finite direct product of finite fields.

MSC2010: 13F10, 13F20, 16P10, 13C05.

Keywords : Principal ideal ring; polynomial ring; finite rings.

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