  In the 1980s Matthias Kreck developed a modified surgery theory with
obstructions in a hardly understood monoid $l_n(Z[\pi])$. This paper presents a
couple of purely algebraic tools to find out whether an element in $l_{2q}(R)$
is "elementary" i.e. whether a Kreck surgery problem leads to an $h$-cobordism
or not.
