nLab Garrett Birkhoff

• Wikipedia entry

Selected writings

Birkhoff's variety theorem (HSP theorem) says that a class of algebras of the same signature is a variety of algebras iff it is closed under homomorphic images (H), subalgebras (S) and small products (P), as proved in

• Garrett Birkhoff, On the structure of abstract algebras, Proc. Cambridge Philos. Soc. 31 (4): 433–454 (1935) doi pdf

The Birkhoff's subdirect representation theorem is proved in

• Garrett Birkhoff, Subdirect unions in universal algebra, Bull. Amer. Math. Soc. 50 (1944), 764-768.

On monoids (not on groupoids in the modern sense of that term):

• Garrett Birkhoff, Hausdorff Groupoids, Annals of Mathematics, Second Series 35 2 (1934) 351-360 [jstor:1968437, doi:10.2307/1968437]

On quantum logic:

• Garrett Birkhoff, John von Neumann: The logic of quantum mechanics, Annals of Mathematics 37 823-843 (1936) [doi:10.2307/1968621, pdf]

On the Birkhoff duality between finite posets and finite distributive lattices

• Garrett Birkhoff, Rings of sets. Duke Mathematical Journal, 3(3):443–454, 1937.

category: people