Ulrich modules over Cohen–Macaulay local rings with minimal multiplicity

Abstract

Abstract Let R be a Cohen–Macaulay local ring. In this paper, we study the structure of Ulrich R-modules mainly in the case where R has minimal multiplicity. We explore generation of Ulrich R-modules and clarify when the Ulrich R-modules are precisely the syzygies of maximal Cohen–Macaulay R-modules. We also investigate the structure of Ulrich R-modules as an exact category.