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The catenary degree of Krull monoids I

Alfred Geroldinger, David J. Grynkiewicz, Wolfgang A. Schmid (2011)

Journal de Théorie des Nombres de Bordeaux

Let H be a Krull monoid with finite class group G such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in an algebraic function field). The catenary degree c ( H ) of H is the smallest integer N with the following property: for each a H and each two factorizations z , z of a , there exist factorizations z = z 0 , ... , z k = z of a such that, for each i [ 1 , k ] , z i arises from z i - 1 by replacing at most N atoms from z i - 1 by at most N new atoms. Under a very mild condition...

The Cayley graph and the growth of Steiner loops

P. Plaumann, L. Sabinina, I. Stuhl (2014)

Commentationes Mathematicae Universitatis Carolinae

We study properties of Steiner loops which are of fundamental importance to develop a combinatorial theory of loops along the lines given by Combinatorial Group Theory. In a summary we describe our findings.

The central heights of stability groups of series in vector spaces

Bertram A. F. Wehrfritz (2016)

Czechoslovak Mathematical Journal

We compute the central heights of the full stability groups S of ascending series and of descending series of subspaces in vector spaces over fields and division rings. The aim is to develop at least partial right analogues of results on left Engel elements and related nilpotent radicals in such S proved recently by Casolo & Puglisi, by Traustason and by the current author. Perhaps surprisingly, while there is an absolute bound on these central heights for descending series, for ascending series...

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