On the cardinality of semistar operations on integral domains

In 1994, Matsuda and Okabe introduced the notion of semistar operation, extending the "classical" concept of star operation. In this article we establish, in finite case, relations among the number of semistar operations and the number of star operations on a domain R, the number of semistar operations on an overring T of R and the Krull dimension of R. As an application, we focus our attention to the case where R is a pullback of T obtained by the classical "D + M" constructions.