Almost-free $E(R)$-algebras and $E(A,R)$-modules

Volume 169 / 2001

Rüdiger Göbel, Lutz Strüngmann Fundamenta Mathematicae 169 (2001), 175-192 MSC: 20K20, 20K30, 16W20. DOI: 10.4064/fm169-2-6

Abstract

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.

Authors

  • Rüdiger GöbelFachbereich 6, Mathematik und Informatik
    Universität Essen
    45117 Essen, Germany
    e-mail
  • Lutz StrüngmannFachbereich 6, Mathematik und Informatik
    Universität Essen
    45117 Essen, Germany
    e-mail

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