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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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votes
Canonical examples of algebraic structures
I think you'll find out very different my example of algebraic structures.
Monoid: the monoid of words over a finite alphabet.
Group: the group of words over a finite alphabet.
Ring: the polinomial …