The equality I2=qI in sequentially Cohen–Macaulay rings

Let R be a sequentially Cohen–Macaulay local ring and assume that or that and e(R)>1. Then the equality I2=qI holds true for every good parameter ideal q of R contained in a sufficiently high power of the maximal ideal m, where I=q:Rm. The structure of the graded rings gr(I)=⊕n⩾0In/In+1, R(I)=⊕n⩾0In, and R′(I)=⊕n∈ZIn associated to I is explored in connection to their sequential Cohen–Macaulayness.