http://www.ncatlab.org/nlab/show/E-infinity-ring
nLab: E_k operad
http://www.ncatlab.org/nlab/show/Barratt-Eccles+operad
See this review for a remark about the interpretation of E-infinity for non-CW homotopy types, e.g. related to profinite groups.
E-infinity stuff. LNM0577: E-infinity ring spaces and E-infty ring spectra
arXiv:0910.3566 H-infinity is not E-infinity from arXiv Front: math.AT by Justin Noel We provide an example of a spectrum with an H-infty structure which does not rigidify to an E_3 structure. It follows that not every H-infinity ring spectrum comes from an underlying E-infinity ring spectrum. After comparing definitions, we obtain this example by applying Sigma^\infty_+ to the counterexample to the transfer conjecture constructed by Kraines and Lada.
arXiv:1103.2764 Diagram spaces and symmetric spectra from arXiv Front: math.AT by Steffen Sagave, Christian Schlichtkrull We present a general homotopical analysis of structured diagram spaces and discuss the relation to symmetric spectra. The main motivating examples are the I-spaces, which are diagrams indexed by finite sets and injections, and J-spaces, which are diagrams indexed by the Grayson-Quillen construction on the category of finite sets and bijections. We show that the category of I-spaces provides a convenient model for the homotopy category of spaces in which every E-infinity space can be rectified to a strictly commutative monoid. Similarly, the commutative monoids in the category of J-spaces model graded E-infinity spaces. Using the theory of J-spaces we introduce the graded units of a symmetric ring spectrum. The graded units detect periodicity phenomena in stable homotopy and we show how this can be applied to the theory of topological logarithmic structures.
nLab page on E-infinity ring