Compact and coprime packedness with respect to star operations

In this paper, we will study the notions of compactly and coprimely packed rings with respect to a star operation of finite type. We extend well-known results and investigate more properties of these notions in different settings such as Prüfer-like settings, Noetherian-like settings and pullbacks. Particular attention is paid to the t-operation as the often usual star operation of finite type. Examples to illustrate the scopes and limits of the results are constructed.