The multiplicity and the Cohen–Macaulayness of extended Rees algebras of equimultiple ideals

Let I be an equimultiple ideal of Noetherian local ring A  . This paper gives some multiplicity formulas of the extended Rees algebras T=A[It,t-1].T=A[It,t-1]. In the case A generalized Cohen–Macaulay, we determine when T   is Cohen–Macaulay and as an immediate consequence we obtain e.g., some criteria for the Cohen–Macaulayness of Rees algebra R(I)R(I) over a Cohen–Macaulay ring in terms of reduction numbers and ideals.