Theories of Modules Closed Under Direct Products

Villemaire, Roger

J. Symbolic Logic, Tome 57 (1992) no. 1, p. 515-521 / Harvested from Project Euclid

Résumé

We generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules $\Pi_F M_i (i \in I)$ is elementarily equivalent to a direct product of ultraproducts of the modules $M_i (i \in I)$.

Publié le : 1992-06-14
Classification:

@article{1183743970,
     author = {Villemaire, Roger},
     title = {Theories of Modules Closed Under Direct Products},
     journal = {J. Symbolic Logic},
     volume = {57},
     number = {1},
     year = {1992},
     pages = { 515-521},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743970}
}

Villemaire, Roger. Theories of Modules Closed Under Direct Products. J. Symbolic Logic, Tome 57 (1992) no. 1, pp.  515-521. http://gdmltest.u-ga.fr/item/1183743970/