# Steenrod operation

From Encyclopedia of Mathematics

The general name for the stable cohomology operations (cf. Cohomology operation) created by N.E. Steenrod for every prime number . The first example is contained in [1]. For this is the Steenrod square , for the Steenrod reduced power . The operations multiplicatively generate the Steenrod algebra modulo 2, while the operations together with the Bockstein homomorphism generate the Steenrod algebra modulo .

#### References

[1] | N.E. Steenrod, "Products of cocycles and extensions of mappings" Ann. of Math. , 48 (1947) pp. 290–320 |

[2] | N.E. Steenrod, D.B.A. Epstein, "Cohomology operations" , Princeton Univ. Press (1962) |

[3] | M.K. Tangora, "Cohomology operations and applications in homotopy theory" , Harper & Row (1968) |

#### Comments

#### References

[a1] | R.M. Switzer, "Algebraic topology - homotopy and homology" , Springer (1975) pp. Chapt. 18 |

[a2] | J.F. Adams, "Stable homotopy and generalized homology" , Univ. Chicago Press (1974) pp. Part III, Chapt. 12 |

**How to Cite This Entry:**

Steenrod operation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Steenrod_operation&oldid=18169

This article was adapted from an original article by Yu.B. Rudyak (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article