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Let R be a subring of the rational numbers ℚ. We recall from [3] that an R-module G is a splitter if . In this note we correct the statement of Main Theorem 1.5 in [3] and discuss the existence of non-free splitters of cardinality ℵ₁ under the negation of the special continuum hypothesis CH.
Rüdiger Göbel, and Saharon Shelah. "An addendum and corrigendum to "Almost free splitters" (Colloq. Math. 81 (1999), 193-221)." Colloquium Mathematicae 88.1 (2001): 155-158. <http://eudml.org/doc/283898>.
@article{RüdigerGöbel2001, abstract = {Let R be a subring of the rational numbers ℚ. We recall from [3] that an R-module G is a splitter if $Ext¹_\{R\}(G,G) = 0$. In this note we correct the statement of Main Theorem 1.5 in [3] and discuss the existence of non-free splitters of cardinality ℵ₁ under the negation of the special continuum hypothesis CH.}, author = {Rüdiger Göbel, Saharon Shelah}, journal = {Colloquium Mathematicae}, keywords = {self-splitting modules; criteria for freeness of modules; splitters; torsion-free Abelian groups}, language = {eng}, number = {1}, pages = {155-158}, title = {An addendum and corrigendum to "Almost free splitters" (Colloq. Math. 81 (1999), 193-221)}, url = {http://eudml.org/doc/283898}, volume = {88}, year = {2001}, }
TY - JOUR AU - Rüdiger Göbel AU - Saharon Shelah TI - An addendum and corrigendum to "Almost free splitters" (Colloq. Math. 81 (1999), 193-221) JO - Colloquium Mathematicae PY - 2001 VL - 88 IS - 1 SP - 155 EP - 158 AB - Let R be a subring of the rational numbers ℚ. We recall from [3] that an R-module G is a splitter if $Ext¹_{R}(G,G) = 0$. In this note we correct the statement of Main Theorem 1.5 in [3] and discuss the existence of non-free splitters of cardinality ℵ₁ under the negation of the special continuum hypothesis CH. LA - eng KW - self-splitting modules; criteria for freeness of modules; splitters; torsion-free Abelian groups UR - http://eudml.org/doc/283898 ER -