Multiplicative Maps from Hz to a Ring Spectrum R - a naive version

TL;DR

This paper investigates the space of multiplicative maps from the Eilenberg-MacLane spectrum to arbitrary ring spectra, generalizing Schwede's approach and introducing a formal group law concept in ring spectra.

Contribution

It generalizes Schwede's method for studying multiplicative maps to any ring spectrum and proposes a new definition of formal group law in this context.

Findings

Defined a formal group law in any ring spectrum

Extended Schwede's approach to a broader class of spectra

Provided new insights into multiplicative maps from HZ to R

Abstract

The paper is devoted to study the space of multiplicative maps from the Eilenberg-MacLane spectrum $H\Z$ to an arbitrary ring spectrum $R$. We try to generalize the approach of Schwede from "Formal groups and stable homotopy of commutative rings", where the special case of the mentioned above problem was solved in full generality. Among other results we propose a definition of a formal group law in any ring spectrum, which might be of interest in its own.