  Ring epimorphisms often induce silting modules and cosilting modules, termed
minimal silting or minimal cosilting. The aim of this paper is twofold.
Firstly, we determine the minimal tilting and minimal cotilting modules over a
tame hereditary algebra. In particular, we show that a large cotilting module
is minimal if and only if it has an adic module as a direct summand. Secondly,
we discuss the behaviour of minimality under ring extensions. We show that
minimal cosilting modules over a commutative noetherian ring extend to minimal
cosilting modules along any flat ring epimorphism. Similar results are obtained
for commutative rings of small homological dimension.

Representation Theory