Local morphisms and modules with a semilocal endomorphism ring
| dc.creator | Facchini, Alberto | |
| dc.creator | Herbera, Dolors | |
| dc.date | 2005-10-05 | |
| dc.date.accessioned | 2026-07-07T06:21:10Z | |
| dc.date.available | 2026-07-07T06:21:10Z | |
| dc.description | An associative ring with 1 is said to be semilocal provided it is semisimple artinian modulo its Jacobson radical, that is, modulo its Jacobson radical it is isomorphic to a finite product of matrices over division rings. Modules with a semilocal endomorphism ring inherit some properties of semisimple modules. For example, they can be decomposed into a finite direct sum of indecomposable submodules, such decomposition is not unique but there are only a finite number of different ones, they cancel from direct sums and they satisfy the n-th root uniqueness property. A ring homomorphism is said to be local if it carries non-units to non-units. Semilocal rings can be characterized as those rings having a local homomorphism to a semisimple artinian ring. In this paper show that local homomorphisms appear frequently in module theory. As a consequence it will follow that many interesting classes of modules, as for example finitely presented modules over semilocal rings, have a semilocal endomorphism ring. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510104 | |
| dc.identifier | http://arxiv.org/abs/math/0510104 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95516 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16D70; 16L30; 18E15 | |
| dc.title | Local morphisms and modules with a semilocal endomorphism ring | |
| dc.type | text |