irreducible n-manifold

An $n$-manifold (http://planetmath.org/TopologicalManifold) $M$ is calledirreducible if for each embedding of a standard $(n-1)$-sphere $S^{n-1}$ in$M$, there is an embedding of a standard $n$-ball (http://planetmath.org/StandardNBall) $D^n$ in $M$ such that theimage of the boundary $\partial D^n$ coincides with the image of$S^{n-1}$.

In case of dimension three it can be proved that each irreducible3-manifold is also a prime (http://planetmath.org/Prime3Manifold) 3-manifold.