Displaying similar documents to “Remarks on factorizations in algebraic number fields”

Generalized morphisms of abelian m-ary groups

Alexander M. Gal'mak (2001)

Discussiones Mathematicae - General Algebra and Applications

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We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m,n)-ring.

Warfield invariants in abelian group rings.

Peter V. Danchev (2005)

Extracta Mathematicae

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Let R be a perfect commutative unital ring without zero divisors of (R) = p and let G be a multiplicative abelian group. Then the Warfield p-invariants of the normed unit group V (RG) are computed only in terms of R and G. These cardinal-to-ordinal functions, combined with the Ulm-Kaplansky p-invariants, completely determine the structure of V (RG) whenever G is a Warfield p-mixed group.

On the asymptotic behavior of some counting functions

Maciej Radziejewski, Wolfgang A. Schmid (2005)

Colloquium Mathematicae

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The investigation of certain counting functions of elements with given factorization properties in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group. In this paper a constant arising from the investigation of the number of algebraic integers with factorizations of at most k different lengths is investigated. It is shown that this constant is positive if k is greater than 1 and that it is also positive if k equals 1 and the class...