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Answer by rschwieb for Name of the following structure?

I think the closest thing to what you are talking about is a semimodule over a semifield which is a commutative monoid acted upon by a semifield. For both the semimodule and the semiring, we've dropped...

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Name of the following structure?

I need the name of the algebraic structure that is like a vector space, but the vectors form a monoid, not a group; the field and the scalar multiplication stays the same.

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