Geodesic
Almost-free $E(R)$-algebras and $E(A,R)$-modules
Rüdiger Göbel 1   ; Lutz Strüngmann 1
1 Fachbereich 6, Mathematik und Informatik Universität Essen 45117 Essen, Germany
Fundamenta Mathematicae, Tome 169 (2001) no. 2, pp. 175-192 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $R$ be a unital commutative ring and $A$ a unital $R$-algebra. We introduce the category of $E(A,R)$-modules which is a natural extension of the category of $E$-modules. The properties of $E(A,R)$-modules are studied; in particular we consider the subclass of $E(R)$-algebras. This subclass is of special interest since it coincides with the class of $E$-rings in the case $R={\mathbb Z}$. Assuming diamond $\diamond $, almost-free $E(R)$-algebras of cardinality $\kappa $ are constructed for any regular non-weakly compact cardinal $\kappa > \aleph _0$ and suitable $R$. The set-theoretic hypothesis can be weakened.
DOI : 10.4064/fm169-2-6
Keywords: unital commutative ring unital r algebra introduce category modules which natural extension category e modules properties modules studied particular consider subclass algebras subclass special interest since coincides class e rings mathbb assuming diamond diamond almost free algebras cardinality kappa constructed regular non weakly compact cardinal kappa aleph suitable set theoretic hypothesis weakened

Rüdiger Göbel  1   ; Lutz Strüngmann  1

1 Fachbereich 6, Mathematik und Informatik Universität Essen 45117 Essen, Germany 
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Rüdiger Göbel; Lutz Strüngmann. Almost-free $E(R)$-algebras and $E(A,R)$-modules. Fundamenta Mathematicae, Tome 169 (2001) no. 2, pp. 175-192. doi: 10.4064/fm169-2-6

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