ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

1. Logic

1991 MS Classification: 03F60, 13P99 Bridges, Douglas, University of Waikato, New Zealand Ideals in constructive ring and Banach algebra theory Let R be a commutative ring with identity and an inequality ≠ . Working within Bishop’s constructive framework, I present a natural definition of maximal ideal, and introduce the property of semidetachability, extending that of detachability (decidable membership). These ideas lead smoothly to proofs of a number of desirable results: for example, a semidetachable maximal ideal in a discrete ring is prime, and a nonzero detachable principal prime ideal in a Euclidean domain is maximal. I also show that a located ideal in a Banach algebra is maximal if and only if it is the kernel of a character. Reference: R. Mines. F. Richman, W. Ruitenburg, A Course in Constructive Algebra, Springer-Verlag, 1988.