CLOSED AND PRIME IDEALS OF WEAK BEZOUT TYPE IN H-INFINITY

[摘要] Let H(is-proportional-to) be the algebra of bounded analytic functions in the open unit disk. An ideal I in H(is-proportional-to) is said to have the weak Bezout property if I contains the greatest common divisor of every pair of elements in I. In Section 1 we give an analytic description of the weak Bezout prime ideals in H(is-proportional-to) in terms of filters. In Section 2 we present a complete characterization of the closed ideals in H(is-proportional-to) which are weak Bezout. In Section 3 we solve the problem of describing all the (nonzero) minimal prime ideals in H(is-proportional-to).

[发布日期] 1991-10-07