ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 13, 94 Cazaran, Jilyana , and Kelarev, Andrei V., Department of Mathematics, University of Tasmania, Australia Sufficient conditions for finite commutative rings to be principal ideal rings and an application to error-correcting codes Let R and S be finite commutative rings having identity elements. First, we give a sufficient condition for the tensor product R ⊗ZZ S to be a principal ideal ring. Second, we describe all quotient rings Q = R[x_{1}, …, x_{n}]/I which are finite commutative principal ideal rings where I is an ideal generated by univariate polynomials f_{i}(x_{i}), 1 ≤ i ≤ n. Third we show how to construct g when rad Q = (g), hence Q is a principal ideal ring. Our results are a continuation of those given in [1]. [1] J. Cazaran and A. V. Kelarev, Generators and weights of polynomial codes, Arch. Math. 69 1997, 479–