Einseinheitengruppen und prime Restklassengruppen in quadratischen Zahlkörpern

AbstractIn this note we calculate explicitly bases of the group of einseinheiten in local quadratic number fields and apply the result for the description of the structure of the prime residue class groups modulo prime divisor powers in an arbitrary quadratic number field

Quadratische ordnungen mit großer Klassenzahl

AbstractAn estimate for the class number of certain quadratic orders from below is given. The method is elementary and applies for imaginary and real quadratic orders of Richaud-Degert and similar types, which usually have large class numbers

Localizing Systems, Module Systems, and Semistar Operations

AbstractWe present the concept of module systems for cancellative monoid. This concept is a common generalization of the notion of an ideal system (as presented by F. Halter-Koch (“Ideal Systems,” Dekker, New York, 1997)) and the notion of a semistar operation (as introduced by A. Okabe and R. Matsuda (Math. J. Toyama Univ.17 (1994), 1–21)). It allows a new insight into the connection between semistar operations and localizing systems (as developed in by M. Fontana and J. A. Huckaba (in “Commutative Rings in a Non-Noetherian Setting” (S. T. Chapman and S. Glanz, Eds.), Kluwer Academic, Dordrecht/Norwell, MA, 2000)), a general theory of flatness (including results of M. Fontana (in “Advances in Commutative Ring Theory” (D. E. Dobbs et al., Eds.), pp. 271–306, Dekker, New York, 1999) and S. Gabelli (in “Advances in Commutative Ring Theory” (D. E. Dobbs et al., Eds.), pp. 391–409, Dekker, New York, 1999)) and a new presentation of the theory of generalized integral closures

A characterization of Krull rings with zero divisors

summary:It is proved that a Marot ring is a Krull ring if and only if its monoid of regular elements is a Krull monoid

The complete integral closure of monoids and domains II

Using geometrical methods we construct primary monoids whose complete integral closure is not completely integrally closed. Such monoids cannot be realized as multiplicative monoids of integral domains with finitely generated groups of divisibility. Complete integral closure, Primary monoids