Coefficient Ideal of Ideals Generated by Monomials

In a commutative Noetherian ring R, the coefficient ideal of I relative to J is the largest ideal 𝔟 for which I𝔟 =J𝔟 when I is integral over J. In this article, we will give a simple algorithm to compute 𝔞(I, J) when I, J are ideals in a polynomial ring R = kX ₁,…, X _d ] generated by monomials and J is a parameter ideal. We use the concept of socle sequence. Also we will show that the reduction number r _J (I) is also computed by our algorithm.