t-closed rings of formal power series

Let A ì BAsubset B be rings. We say that A is t-closed in B, if for each a ? Aain A and b ? Bbin B such that b²-ab,b³-ab² ? Ab^2-ab,b^3-ab^2in A, then b ? Abin A. We present a sufficient condition for the ring A[[X₁,?,X_n]]A[[X_1,ldots ,X_n]] to be t-closed in B[[X₁,?,X_n]]B[[X_1,ldots ,X_n]]. By an example, we show that our condition is not necessary. Even though the question is still open, some important cases are treated. For example, if A ì BAsubset B is an integral extension, or if A is p-injective, then A[[X₁,?,X_n]]A[[X_1,ldots ,X_n]] is t-closed in B[[X₁,?,X_n]]B[[X_1,ldots ,X_n]] if and only if A is t-closed in B.