introduction For an elliptic curve that is fbr a complete non-singular algebraic curve of genus 1 there is an abelian structure and it s law of compositio11 For genus1 case we may cOnsider linear transfbrmation on the divisor class group defined by a certain cycle or divisor of the double or triple product of the curve The purpose of this paper is to study the relation between the dirtsum dom position of the divisor class group and the decompositioof Jacobian variety At first we construct a certain Lie ring on the divisor dass group 1 On a certain type of Lie ring Let Z(and C be the rational integerg the rational number 6eld and the complex number field resptively Let C be a complete non-singular algebraic curve defined on theeld which is finitely generated over the prime 6eld Let g be the divisoclass group of C modulo by the groug of aU divisors linearly equivalent to zero And let gbe the subgroup of g consisting of aclasses that containK-rational divisor where K isnitely generated
Seishi WADA (Fri,) studied this question.