Characteristic-free test ideals

Tight closure test ideals have been central to the classification of singularities in rings characteristic p > 0 p>0 , and via reduction equal 0 as well. Their properties applications described by Schwede Tucker [Progress commutative algebra 2, Walter de Gruyter, Berlin, 2012]. In this paper, we extend notion a ideal arbitrary operations, particularly those coming from big Cohen-Macaulay modules algebras, prove that it shares key tight ideals. Our main results show how these can be used give characteristic-free singularities, including few specific on mixed case. We also compute examples