On the integral closure of ideals.
On the irreducibility of pure difference binomials.
On the Jacobian criterion of formal smoothness.
We give a short proof of the Jacobian criterion of formal smoothness using the Lichtenbaum-Schlessinger cotangent complex.
On the module of homomorphisms on finitely generated projective modules
On the reduction of Kronecker's modular systems whose elements are functions of two and three variables.
On the ring of quotients of a noetherian commutative ring with respect to the Dickson topology
On the structure and arithmetic of finitely primary monoids
On the structure of certain normal ideals
On the Transitvity of regular differential Forms.
On valuation spectra
One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal
Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate quadratic...
Outer automorphisms of endomorphism algebras
Commutative rings over which no endomorphism algebra has an outer automorphism are studied.