I have expanded the section *Snaith theorem – For complex topological K-theory* by adding a fair amount of the basic details that go into the construction of the ring spectrum homomorphism

itself.

]]>I have added at bit more of a remark along these lines:

*Snaith-like theorem for Morava E-theories*

also added a brief pointer along these lines to *Morava E-theory* itself.

In

- Craig Westerland,
*A higher chromatic analogue of the image of J*(arXiv:1210.2472)

is a tower of Snaith theorems for Morava $E$-theories. Have added a pointer to this to the entry.

]]>The only other variant that I have seen is for periodic algebraic cobordism and algebraic K-theory, in Gepner-Snaith 08.

Concerning notation for periodic $MU$: how about $PMU$? I have changed it to that in the entry.

]]>What about S[BU] before localization? Is it equivalent to MU or some well-known spectrum?

Also, is there an analog for real K-theory?

Something along the lines of ko=S[W] for some W (a naive guess would be W=BZ/2)

and KO=ko[β^{−1}], where β is the Bott element for real K-theory (in particular, it has degree 8). ]]>