2
votes
1answer
137 views

What motivates the study of Abelian groups?

Monoids arise naturally as endomorphism monoids, and groups arise naturally as automorphism groups. These are among the primary motivators for their study, in my opinion. What are the (main) ...
5
votes
5answers
1k views

Motivation for the Tensor Product [duplicate]

I've already asked about the definition of tensor product here and now I understand the steps of the construction. I'm just in doubt about the motivation to construct it in that way. Well, if all that ...
16
votes
2answers
590 views

Why are modular lattices important?

A lattice $(L,\leq)$ is said to be modular when $$(\forall a,b\in L) x \leq b \implies x \vee (a \wedge b) = (x \vee a) \wedge b,$$ where $\vee$ is the join operation, and $\wedge$ is the meet ...