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# Homology, Homotopy and Applications

## Volume 3 (2001)

### Number 2

### Volume of a Workshop at Stanford University

### Idempotents and Landweber exactness in brave new algebra

Pages: 355 – 359

DOI: http://dx.doi.org/10.4310/HHA.2001.v3.n2.a4

#### Author

#### Abstract

We explain how idempotents in homotopy groups give rise to splittings of homotopy categories of modules over commutative $S$-algebras, and we observe that there are naturally occurring equivariant examples involving idempotents in Burnside rings. We then give a version of the Landweber exact functor theorem that applies to $MU$-modules.

#### Keywords

Brown-Peterson spectrum, Landweber exact functor theorem, complex cobordism, $E_{\infty}$ ring spectrum

#### 2010 Mathematics Subject Classification

55N20, 55N91, 55P43