Torsion-free modules with nearly unique endomorphism algebras
W May - Communications in Algebra, 2003 - Taylor & Francis
W May
Communications in Algebra, 2003•Taylor & Francis… As partial justification for this remark, if we restrict consideration to reduced p-local
abelian groups, then May (Citation1992) shows that those groups with torsion-free rank
nonzero and smaller than 2 ℵ 0 will share their endomorphism algebras with infinitely many
pairwise nonisomorphic groups. At the other extreme, it is not at all clear whether there can
exist torsion-free abelian groups which share their endomorphism algebra with at most
finitely many other pairwise nonisomorphic torsion-free abelian groups. Generalizing to the …
abelian groups, then May (Citation1992) shows that those groups with torsion-free rank
nonzero and smaller than 2 ℵ 0 will share their endomorphism algebras with infinitely many
pairwise nonisomorphic groups. At the other extreme, it is not at all clear whether there can
exist torsion-free abelian groups which share their endomorphism algebra with at most
finitely many other pairwise nonisomorphic torsion-free abelian groups. Generalizing to the …
Abstract
Let R be a discrete valuation domain and n ≥ 1. If the completion of R contains at least n algebraically independent elements over R, then there exists a torsion-free module M such that End R M is isomorphic to End R N for exactly 2 n pairwise nonisomorphic modules N.
Taylor & Francis Online以上显示的是最相近的搜索结果。 查看全部搜索结果