Abstract
The calculus of fractions is an important construction in commutative algebra. One might expect that it would correspond to an important construction in the category of commutative algebras. But one cannot see which one a priori. If it is true that an algebra of fractions is a universal algebra making a set of elements invertible, one still has to know what corresponds to the invertible elements. This new universal construction will be revealed and we will make an extensive study of it in the category of commutative unitary rings. Alongside the rings of fractions we will see emerging ‘rings of quotients’.
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