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Let R be a commutative Noetherian ring and I be a one dimensional ideal of the Laurent polynomial ring R[X,X] that contains a doubly monic polynomial. Define I(1) :=< {f(1) : f ∈ I} >. Let I/I be genereted by n ≥ 2 elements over R[X,X]/I . Then any set of n generators of I(1) over R may not be lifted to a set of n generators of I over R[X,X] by describing an example of one dimensional ideal. AMS Subject Classification: 13E05, 13E15, 13C10

HOMOTOPY SECTIONS OF ONE DIMENSIONAL IDEALS OVER A LAURENT POLYNOMIAL RING