# Strongly indecomposable H-spaces

#### Abstract

In this paper we study loop near-rings that arise as endomorphisms of connected H-spaces, and apply the theory of rings and near-rings to obtain decomposition theorems for H-spaces. We first prove that local loop-near rings correspond to strongly indecomposable H-spaces, and derive a uniqueness theorem for decompositions of H-spaces that is analogous to the classical Krull–Schmidt–Remak– Azumaya theorem for modules. Then we show that some naturally defined homomorphisms are idempotent-lifting, which implies that certain indecomposable idempotents are in fact local. As a consequence we prove that in the category of finite p-local H-spaces indecomposable spaces are automatically strongly indecomposable.

### Cite this paper

@inproceedings{Franeti2011StronglyIH, title={Strongly indecomposable H-spaces}, author={Damir Franeti{\vc} and Petar Pavesic}, year={2011} }