Annihilator chain conditions in polynomial rings

Ramon Antoine¹

Universitat Autonoma de Barcelona

We study the behavior of annihilator chain conditions when passing from a ring $R$ to the polynomial ring $R[x]$ and focus in the particular case of finite dimensional rings, that is, the Goldie condition. Hence, for any finite field $K$, we give an example of a commutative Goldie $K$-algebra $R$ for which $R[X]$ is not Goldie. This generalizes a result of J.W. Kerr.

Footnotes

... Antoine¹

joint work with Ferran Cedó