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About Direct Summands of Projective Modules Over Laurent Polynomial Rings

About Direct Summands of Projective Modules Over Laurent Polynomial Rings

Suppose i is a local ring and R = A[X, X-1] is a Laurent polynomial ring.We prove that for projective Ä-modules P and Q with rank Q < rank P , if Q, is a direct summand of Pf for a doubly monic polynomial / then Q is also a …