Tensor Product as a Universal Object (Category Theory & Module Theory)
IntroductionIt is quite often to see direct sum or direct product of groups, modules, vector spaces. Indeed, for modules over...
Rings of Fractions and Localisation
Is perhaps the most important technical tools in commutative algebra. In this post we are covering definitions and simple pro...
The Grothendienck Group
Free groupLet $A$ be an abelian group. Let $(e_i)_{i \in I}$ be a family of elements of $A$. We say that this family is a bas...