Generalized E-Rings
| dc.creator | Göbel, Rüdiger | |
| dc.creator | Shelah, Saharon | |
| dc.creator | Strüngmann, Lutz | |
| dc.date | 2004-04-15 | |
| dc.date.accessioned | 2026-07-07T05:07:27Z | |
| dc.date.available | 2026-07-07T05:07:27Z | |
| dc.description | A ring R is called an E-ring if the canonical homomorphism from R to the endomorphism ring End(R_Z) of the additive group R_Z, taking any r in R to the endomorphism left multiplication by r turns out to be an isomorphism of rings. In this case R_Z is called an E-group. Obvious examples of E-rings are subrings of Q. However there is a proper class of examples constructed recently. E-rings come up naturally in various topics of algebra. This also led to a generalization: an abelian group G is an E-group if there is an epimorphism from G onto the additive group of End(G). If G is torsion-free of finite rank, then G is an E-group if and only if it is an E-group. The obvious question was raised a few years ago which we will answer by showing that the two notions do not coincide. We will apply combinatorial machinery to non-commutative rings to produce an abelian group G with (non-commutative) End(G) and the desired epimorphism with prescribed kernel H. Hence, if we let H=0, we obtain a non-commutative ring R such that End(R_{Z}) cong R but R is not an E-ring. | |
| dc.identifier | https://arxiv.org/abs/math/0404271 | |
| dc.identifier | http://arxiv.org/abs/math/0404271 | |
| dc.identifier | in: {Rings, modules, algebras, and abelian groups} (2004) 291--306 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70863 | |
| dc.subject | Logic | |
| dc.subject | Group Theory | |
| dc.subject | Rings and Algebras | |
| dc.title | Generalized E-Rings | |
| dc.type | text |