The algebraic theory of Kreck surgery

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.