Programming Language Theory and Abstract Algebra Are there any applications of Abstract Algebra to Programming Language Theory? Is there anything that would be useful in language design and compiler implementation?
Algebra in the classical sense of the word is used in modeling of computational effects as algebraic operations, see for example these slides by Gordon Plotkin, or you can read real papers and Ph.D. theses, if you actually meant to ask the question.

And to blow my own horn, have a look at Eff and read about it, a language designed around the idea that computational effects are algebraic operations and that handlers are homomorphisms of algebras.