The Conductor of one-dimensional Gorenstein Rings in their blowing-up.
The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.
The article studies the cubic mapping graph of , the ring of Gaussian integers modulo . For each positive integer , the number of fixed points and the in-degree of the elements and in are found. Moreover, complete characterizations in terms of are given in which is semiregular, where is induced by all the zero-divisors of .
Let X be a quotient surface singularity, and define as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture...
In this paper the concept of the second submodule (the dual notion of prime submodule) is introduced.