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In mathematics, a P-irreducible manifold is a 3-manifold that is irreducible and contains no 2-sided ${\displaystyle \mathbb {R} P^{2}}$ (real projective plane). An orientable manifold is P-irreducible if and only if it is irreducible. Every non-orientable P-irreducible manifold is a Haken manifold.

References

1. Hazewinkel, Michiel (2001), Encyclopaedia of Mathematics, Supplement III, Volume 13, Springer, p. 183, ISBN 9781556080104.
2. Rassias, George M.; Stratopoulos, George (1989), Geometry and Topology, World Scientific, p. 33, ISBN 9789971506780.

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