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I've just started learning about rings. Rings are one additive abelian group strung together, through the associative law, with another structured operation.

Couldn't we continue stringing together operations in this manner (a multi-operation associative law)? Would what I'm thinking be encompassed by the ring definition through something I'm missing? If not, is this done and, if so, do useful objects come out of it?

3 Answers 3