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

Abstract: Let I be an equimultiple ideal of Noetherian local ring A. This paper gives some multiplicity formulas of the extended Rees algebras 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 over a Cohen–Macaulay ring in terms of reduction numbers and ideals. [Copyright &y& Elsevier]