I would like to know of some uses of algebraic structures to study computer science. Parallels of what I am looking for would be stuff like the fundamental group/homology/cohomology in topology and class fields in number theory where groups/rings are used to represent information about the object we are studying. I am not asking for examples like the graph isomorphism problem. Is there any equivalent in computer science? I would very much appreciate references too.
2026-04-07 11:12:19.1775560339
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Abstract Algebra in analyzing computer science
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I'm not sure this is what you're interested in properly, but this book shows "applications" of abstract algebra, and a nice unusual example of finite semigroup (see this later answer), in the context of computing machines.
Look at Maurice Herlihy's work on applications of topology in distributed computing. He won a Turing award for it. :)