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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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When is it okay to intersect infinite families of proper classes?
Here is an example of a family of classes of rings which you couldn't intersect: The class $A_n$ consists of all rings of power greater than n and the rings of cardinality $k≤n$ such that $ϕ_k$, where …