What does this symbol mean in commutative algebra

commutative-algebraelementary-set-theory

(Algebraic Geometry and commutative algebra – Bosch – page 16)

I could not find the symbol in the glossary at the end of the book. What does it mean ?

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I cannot see it in my reference manual either (Commutative Algebra with a view towards algebraic geometry – Eisenbud)

Best Answer

Its the disjoint union from set theory. Each element of $\text{Spec } R$ maps into a different set from the disjoint union.

In category theory this symbol can sometimes be a coproduct, but in this situation it’s not.

Added: Of course disjoint union is the coprduct in sets, but you hardly see all those rings/ $R$-modules and think “category of sets”. This tradition of confusing young scholars of scheme theory goes back, at least to Hartshorne’s book.

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