[Verse 1]
Two operations dancing in harmony's embrace
Addition forms an abelian group in this space
Multiplication follows associative law
Distributive properties without any flaw
[Chorus]
Ring it out, ring it true
Set R with operations two
Plus and times must satisfy
Four conditions reaching high
Abelian group for addition's song
Associative multiplication strong
Distributive laws both left and right
Ring structure shining crystal bright
[Verse 2]
Integers, rationals, reals and complex too
Modular arithmetic in Z mod n's view
Polynomial rings with variables free
Matrix rings in dimensions we see
[Chorus]
Ring it out, ring it true
Set R with operations two
Plus and times must satisfy
Four conditions reaching high
Abelian group for addition's song
Associative multiplication strong
Distributive laws both left and right
Ring structure shining crystal bright
[Bridge]
Commutative when ab equals ba
Integral domains have no divisors of zero's law
Division rings where inverses exist
Fields are commutative on this list
Gaussian integers a plus bi
Ring theory reaching for the sky
[Verse 3]
Distributive magic a times b plus c
Equals ab plus ac perfectly
Left and right both ways it flows
Mathematical beauty that grows
[Chorus]
Ring it out, ring it true
Set R with operations two
Plus and times must satisfy
Four conditions reaching high
Abelian group for addition's song
Associative multiplication strong
Distributive laws both left and right
Ring structure shining crystal bright
[Outro]
Usually there's identity one
Ring theory's journey has begun
Four axioms guide the way
In algebraic structures' play