Orders in quadratic fields, I
Copyright policy )Orders in quadratic fields, I
In Part I [ibid. 69, 45-48 (1993; Zbl 0795.11056)], the author gave a criterion for an arbitrary order to have class group generated by ambiguous ideals and also made a conjecture related to that criterion. Afterwards, however, counterexamples to the conjecture were found [cf. Part III, ibid. 70, 176-181 (1994; Zbl 0809.11064)]. In this paper, he provides its revised version with a simple proof which gives a necessary and sufficient condition for the class group of a complex quadratic field to have exponent at most 2 in terms of the split primes less than the Minkowski bound.
- University of Calgary Canada
primitive ideals, Class groups and Picard groups of orders, ambiguous classes of a complex quadratic order, Other algebras and orders, and their zeta and \(L\)-functions, 11R29, Class numbers, class groups, discriminants, ambiguous ideals, class group, 11R65, Quadratic extensions, 11R11, Primes represented by polynomials; other multiplicative structures of polynomial values, prime-producing quadratic polynomials, ideal class group, quadratic orders, exponent, reduced ideals, complex quadratic field
primitive ideals, Class groups and Picard groups of orders, ambiguous classes of a complex quadratic order, Other algebras and orders, and their zeta and \(L\)-functions, 11R29, Class numbers, class groups, discriminants, ambiguous ideals, class group, 11R65, Quadratic extensions, 11R11, Primes represented by polynomials; other multiplicative structures of polynomial values, prime-producing quadratic polynomials, ideal class group, quadratic orders, exponent, reduced ideals, complex quadratic field
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!