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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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Name for union of upsets/downsets
Set of lower bounds in poset is defined like $ A^l = \{ x \in P : \forall a \in A . x \le a \} = \bigcap_{a \in A} \{ x \in P : x \le a \}$.
Is there in literature a name for union $ \bigcup_{a \in …