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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.
5
votes
About enveloping algebras of direct sums
I'm adding my comment as a partial answer, as discussed there; this is a reformulation of point 2 that has been added to the question.
Let $\mathcal L$ be the category of Lie $R$-algebras. Assume tha …