@MartinSleziak I would say it also depends on what you want to do with these algebras. Maybe modules-algebras would encompass what you're looking for. For example ring-theory, representation-theory contain questions that would fit that tag (and yours).
I see :) I share that feeling that doing something about it would be useful (maybe even necessary), however I couldn't come up with a tag proposal that I really liked.
@JM I plea guilty of that. I gotta go for a while, maybe we'll talk again tomorrow morning (for you), afterwards I'll be gone for about a week. So, see you later or next week.