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pro vyhledávání: '"Lorensen, Karl"'
Autor:
Lorensen, Karl, Öinert, Johan
We study path rings, Cohn path rings, and Leavitt path rings associated to directed graphs, with coefficients in an arbitrary ring $R$. For each of these types of rings, we stipulate conditions on the graph that are necessary and sufficient to ensure
Externí odkaz:
http://arxiv.org/abs/2404.07093
Autor:
Lorensen, Karl, Öinert, Johan
A ring $R$ has {\it unbounded generating number} (UGN) if, for every positive integer $n$, there is no $R$-module epimorphism $R^n\to R^{n+1}$. For a ring $R=\bigoplus_{g\in G} R_g$ graded by a group $G$ such that the base ring $R_1$ has UGN, we iden
Externí odkaz:
http://arxiv.org/abs/2201.04087
Autor:
Kropholler, Peter, Lorensen, Karl
A ring $R$ satisfies the {\it strong rank condition} (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that the base ring $R_1$ is a domain.
Externí odkaz:
http://arxiv.org/abs/1901.10001
Autor:
Kropholler, Peter, Lorensen, Karl
We prove that every finitely generated, virtually solvable minimax group can be expressed as a homomorphic image of a virtually torsion-free, virtually solvable minimax group. This result enables us to generalize a theorem of Ch. Pittet and L. Saloff
Externí odkaz:
http://arxiv.org/abs/1510.07583
Autor:
Lorensen, Karl
We define a class $\mathcal{U}$ of solvable groups of finite abelian section rank which includes all such groups that are virtually torsion-free as well as those that are finitely generated. Assume that $G$ is a group in $\mathcal{U}$ and $A$ a $\mat
Externí odkaz:
http://arxiv.org/abs/1406.3731
Autor:
Kropholler, Peter, Lorensen, Karl
Assume that $G$ is a virtually torsion-free solvable group of finite rank and $A$ a $\mathbb ZG$-module whose underlying abelian group is torsion-free and has finite rank. We stipulate a condition on $A$ that ensures that $H^n(G,A)$ and $H_n(G,A)$ ar
Externí odkaz:
http://arxiv.org/abs/1303.5005
Autor:
Lorensen, Karl
Publikováno v:
Bull. Aust. Math. Soc. 86 (2012), 254-265
Assume $G$ is a solvable group whose elementary abelian sections are all finite. Suppose, further, that $p$ is a prime such that $G$ fails to contain any subgroups isomorphic to $C_{p^\infty}$. We show that if $G$ is nilpotent, then the pro-$p$ compl
Externí odkaz:
http://arxiv.org/abs/1103.1610
Autor:
Lorensen, Karl
Assume $G$ is a polycyclic group and $\phi:G\to G$ an endomorphism. Let $G\ast_{\phi}$ be the ascending HNN extension of $G$ with respect to $\phi$; that is, $G\ast_{\phi}$ is given by the presentation $$G\ast_{\phi}= < G, t \ |\ t^{-1}gt = \phi(g)\
Externí odkaz:
http://arxiv.org/abs/1009.2645
Akademický článek
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Autor:
Lorensen, Karl
Publikováno v:
J. Pure Appl. Algebra 214 (2010), 6-14
For any prime $p$ and group $G$, denote the pro-$p$ completion of $G$ by $\hat{G}^p$. Let $\mathcal{C}$ be the class of all groups $G$ such that, for each natural number $n$ and prime number $p$, $H^n(\hat{G^p},\mathbb Z/p)\cong H^n(G, \mathbb Z/p)$,
Externí odkaz:
http://arxiv.org/abs/0809.3046