Indecomposable almost free modules - the local case
| dc.creator | Göbel, Rüdiger | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2000-11-22 | |
| dc.date.accessioned | 2026-07-07T04:38:46Z | |
| dc.date.available | 2026-07-07T04:38:46Z | |
| dc.description | Let R be a countable, principal ideal domain which is not a field and A be a countable R-algebra which is free as an R-module. Then we will construct an aleph_1-free R-module G of rank aleph_1 with endomorphism algebra End_RG=A . Clearly the result does not hold for fields. Recall that an R-module is aleph_1-free if all its countable submodules are free, a condition closely related to Pontryagin's theorem. This result has many consequences, depending on the algebra A in use. For instance, if we choose A=R, then clearly G is an indecomposable `almost free' module. The existence of such modules was unknown for rings with only finitely many primes like R=Z_{(p)}, the integers localized at some prime p. The result complements a classical realization theorem of Corner's showing that any such algebra is an endomorphism algebra of some torsion-free, reduced R-module G of countable rank. Its proof is based on new combinatorial-algebraic techniques related with what we call rigid tree-elements coming from a module generated over a forest of trees. | |
| dc.identifier | https://arxiv.org/abs/math/0011182 | |
| dc.identifier | http://arxiv.org/abs/math/0011182 | |
| dc.identifier | Canadian Journal of Mathematics, 50 (1998):719--738 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60413 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Commutative Algebra | |
| dc.subject | Group Theory | |
| dc.subject | Logic | |
| dc.title | Indecomposable almost free modules - the local case | |
| dc.type | text |