Vol. 51, No. 1, 1974

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On separable polynomials over a commutative ring

Frank Rimi DeMeyer

Vol. 51 (1974), No. 1, 57–66

Separable polynomials over an arbitrary commutative ring are studied. Given any separable polynomial p(X) over the commutative ring R one can find a “splitting ring” for p(X) which is a finitely generated normal separable extension of R generated by roots of p(X). A polynomial closure Λ of R generated by roots of separable polynomials is constructed. Any separable polynomial over Λ factors into linear factors in Λ. A Galois theory for such extensions is discussed. Applications to separable extensions of von Neumann regular rings and the Brauer group are given.

Mathematical Subject Classification 2000
Primary: 13B25
Received: 8 November 1972
Published: 1 March 1974
Frank Rimi DeMeyer