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Berwick was an algebraist who worked on the problem of computing an integral basis for the algebraic integers in a simple algebraic extension of the rationals. He also suudied ideals in the ring of algebraic integers. His book Integral Bases published in 1927 is a significant contribution.
The existence of such a basis can be easily proved but practical methods to compute such a basis are much harder. The heavy numerical computationals involved in Berwick's work kept it outside the mainstream of algebraic number theory.
Berwick also gave, in 1915, necessary and sufficient conditions for a quintic equation to be soluble by radicals.
References (2 books/articles)