abstract
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On the cardinality of smallest spanning sets of rings

Nadia Boudi and Lorenz Halbeisen

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Let *R*=(R,+, · ) be a ring. Then a subset Z of R is
called *spanning* if the *R*-module generated by Z is equal
to the ring *R*. A spanning set Z is called *smallest* if
there is no spanning set of smaller cardinality than Z. It will be
shown that the cardinality of a smallest spanning set of a ring is
not always decidable. In particular, a ring will be constructed such
that the cardinality of a smallest spanning set of this ring depends
on the underlying set theoretic model.