We introduce an algebra for the Alexander-Conway polynomial.
 The Jones polynomial of a closed braid may be obtained from
 a representation of the Temperley-Lieb algebra.
 We define a new algebra by a modification of the definition
 of the Temperley-Lieb algebra.
 We show that the Alexander-Conway polynomial may be obtained
 from a representation of this algebra.
 Furthermore we introduce a bracket polynomial for the
 Alexander-Conway polynomial and investigate it.
 We obtain a construction of the Alexander-Conway polynomial
 through a smoothing decomposition.