Computing j-multiplicity ant its application

虽然局部环的重数理论是交换代数中非常重要的经典理论，但它只适用于包含极大理想的某些幂的理想。因此，一个广义的不变量命名为“j-多重性”。只是，它的价值，实在是难以计算。在本研究中，我们建立了一个计算理想的j重数的实用方法。

Although the theory of multiplicity of local rings is very important as a classical theory in commutative algebra, but it can be applied to only ideals containing some power of the maximal ideal. Hence a generalized invariant named "j-multiplicity" was introduced. However, it was really difficult to compute its value. In this research, we established a practical method for computing the j-multiplicity of a given ideal.