"Socialism" is loosely defined as "social ownership and democratic control of the means of production."
That is more like the definition of "communism".
It is the dictionary definition of socialism in English.
If you want a different meaning, use a different word, or qualify your usage.
Socialism definitely does not imply state ownership
The above quote states control, not necessarily ownership. "Control or regulation" would also be an okay definition, but this seems redundant to me.