[Verse 1] Take two modules M and N, crossing paths where rings collide Build a bridge with symbols drawn, m tensor n as your guide But these symbols must obey the rules that keep them bound Distributive laws and scalar tricks make bilinear ground [Chorus] Tensor products, tensor products Weaving modules into one Left distributes, right distributes Scalars jump from side to side It's the universal language Where bilinear maps reside M tensor N, the bridge between Two worlds unified [Verse 2] When addition meets a tensor, watch it split and multiply Left side sum becomes two terms, right side does the same reply But the magic happens when a scalar finds its way Moves from left to right at will, that's the tensor way [Chorus] Tensor products, tensor products Weaving modules into one Left distributes, right distributes Scalars jump from side to side It's the universal language Where bilinear maps reside M tensor N, the bridge between Two worlds unified [Bridge] Universal property speaks the truth we need to know Every bilinear map factors through this special flow R tensor M gives back just M, identity revealed Direct sums become direct sums when tensor rules are sealed [Verse 3] Cyclic groups dance strange ballet when integers collide Z mod m with Z mod n makes gcd their guide The greatest common divisor holds the final key To unlock what remains when torsion breaks free [Outro] Most general construction, bilinear and true Tensor products show the way that modules can renew In the algebra of structures, this bridge will always stand M tensor N forever, algebraic promised land
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