Let A be a superalgebra endowed with a pseudoinvolution ∗ over an algebraically closed field of characteristic zero. If A satisfies an ordinary non-trivial identity, then its graded ∗-codimension sequence \(c_{n}^{*}(A)\), n = 1,2,…, is exponentially bounded (Ioppolo and Martino (Linear Multilinear Algebra 66(11), 2286–2304 2018). In this paper we capture this exponential growth giving a positive answer to the Amitsur’s conjecture for this kind of algebras. More precisely, we shall see that the \(\lim _{n \rightarrow \infty } \sqrt [n]{c_{n}^{*}(A)}\) exists and it is an integer, denoted \(\exp ^{*}(A)\) and called graded ∗-exponent of A. Moreover, we shall characterize superalgebras with pseudoinvolution according to their graded ∗-exponent.

设A是在特征为零的代数封闭域上具有拟对合*的超代数。如果A满足普通的非平凡身份，则其渐变∗余阶序列\（c_ {n} ^ {*}（A）\），n = 1,2，…，按指数有界（Ioppolo和Martino（线性Multilinear Algebra 66（11），2286–2304 2018）。在本文中，我们捕获了这种指数增长，为此类代数对Amitsur的猜想给出了肯定的答案。更确切地说，我们将看到\（\ lim _ {n \ rightarrow \ infty} \ sqrt [n] {c_ {n} ^ {*}（A）} \）存在，它是一个整数，表示为\（\ exp ^ {*}（A）\）并被称为∗ -exponent的一。此外，我们将根据伪代数的分级*指数来刻画超级代数的特征。