Department of Mathematics, Kobe University, 1-1, Rokkodai-cho, Nada-ku, Kobe 657, Japan
Abstract:
Shibuya proved that any union of two nontrivial knots without local knots is a prime knot. In this note, we prove it in a general setting. As an application, for any nontrivial knot, we give a knot diagram such that a single unknotting operation on the diagram cannot yield a diagram of a trivial knot.