[Verse 1]
Free modules dance with perfect symmetry
Direct sums of R, stacked endlessly
Every element finds its basis home
Linear independence carved in stone
F isomorphic to R to the n
Where generators rule and freedom wins
[Chorus]
Exact sequences, perfect handoff chain
Image equals kernel, no loss no gain
What flows out becomes what flows in
Zero to A to B to C again
Splitting when the middle breaks apart
Free modules beating at algebra's heart
[Verse 2]
Homomorphisms linking module to module
Maps preserve the structure, that's the model
Kernel catches elements sent to zero
Image shows the range of our hero
Chain them up in sequence so divine
Where one map ends, the next begins its line
[Chorus]
Exact sequences, perfect handoff chain
Image equals kernel, no loss no gain
What flows out becomes what flows in
Zero to A to B to C again
Splitting when the middle breaks apart
Free modules beating at algebra's heart
[Bridge]
Short exact means injection starts the show
Surjection ends where all the outputs go
C looks like B mod A when dust settles down
But splitting? That depends on what ring you found
Over fields they split like morning light
Over integers they might stay tight
[Verse 3]
Information flows without any waste
Every arrow lands in perfect place
Zero to Z to Z to Z mod two
Doesn't split though sequence runs true
Bass line pumping through the exact chain
Module theory driving through my brain
[Chorus]
Exact sequences, perfect handoff chain
Image equals kernel, no loss no gain
What flows out becomes what flows in
Zero to A to B to C again
Splitting when the middle breaks apart
Free modules beating at algebra's heart
[Outro]
Free and exact, the algebra code
Basis vectors on the module road
Handoff perfect, nothing left behind
Exact sequences, peace of mind