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In On Utumi's ring of quotients, Canad. J. Math. 15(1963), 363-370, J. Lambek says: As a matter of historical record, the minimal injective extension of a module is a special case of the "algebraic ...

When defining algebraic structures (like monoids, groups, etc...), are there some constraints on the shape of the axioms, for the structure to have good properties that we implicitly use in many ...