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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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Binomial Expansion for non-commutative setting
See a paper entitled "Binomial expansion for non-commutative
operators" written by Martin Pépin and Lucas Verney (February 3, 2016).