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We study the question if projective modules over formal Laurent series ringsare extended. We relate this question to the Bass-Quillen conjecture forcommutative regular local rings and to the Hermite ring conjecture for allcommutative local rings. Using our result about projective modules over formalLaurent series rings, we prove a reduction step for the Hermite ringconjecture. We show that the Hermite ring conjecture holds for all commutativelocal rings if and only if it holds for complete intersection rings which arealso unique factorization domains.

Formal Laurent series rings and the Hermite ring conjecture