Projective modules over rings with many units

McDonald, B. R.; Waterhouse, William C.

doi:10.1090/S0002-9939-1981-0627668-7

Projective modules over rings with many units
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by B. R. McDonald and William C. Waterhouse PDF

Proc. Amer. Math. Soc. 83 (1981), 455-458 Request permission

Abstract:

Let $R$ be a commutative ring. Assume that every polynomial whose values generate the unit ideal actually takes on an invertible value. Then projective $R$-modules split into cyclic summands, and those of constant rank are free.

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