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it is known, abstract algebra studying about algebraic structure. algebraic structure is non-empty set with one or more binary operation and satisfy some axioms. for example group,ring,field,etc.
its often write "let R be an algebra with relation...." or "let R be an algebra over field S"
what the meaning of algebra? what's the different from algebraic structure?
question: let R be algebra over field Q (rational), with relation n element of natural number. R is a ring or not??