arXiv subjects
Publications and source records attributed to Mehran Rahimi.
Some basic properties of Ulrich modules are studied and it is proved that Ulrich modules in Cohen-Macaulay local rings are decomposable. As a result, some characterizations proved for rings having minimal multiplicity, and some properties for ideals which are Ulrich as module is discussed.
The aim of this note is to study the class of one dimensional Cohen-Macaulay local rings, $(R, \mathfrak{m})$ say, possessing a canonical ideal $K$ which is a reduction of $\mathfrak{m}$. We call $R$ to have canonical reduction $K$. We show that the class of rings with canonical reductions contains the class of almost Gorenstein rings and establish its relation with rings obtained by idealizations and also with numerical semigroup rings.