A criterion for detecting m-regularity.
A criterion for rings which are locally valuation rings
Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semisimple if and only if every R-module is cyclically pure...
A factorization theorem for the polar of a curve with two branches
A Few Remarks on the Mohan Kumar Theorem
We give a simple geometric proof of Mohan Kumar's result about complete intersections.
A fibre criterion for a polynomial to belong to an ideal.
A finite ring polynomial.
A General Theory of Almost Factoriality.
A generalization of semiflows on monomials
Let be a field, and the set of monomials of . It is well known that the set of monomial ideals of is in a bijective correspondence with the set of all subsemiflows of the -semiflow . We generalize this to the case of term ideals of , where is a commutative Noetherian ring. A term ideal of is an ideal of generated by a family of terms , where and are integers .
A Generalization of the Class Group.
A geometric approach to the Jacobian Conjecture in ℂ²
We consider polynomial mappings (f,g) of ℂ² with constant nontrivial jacobian. Using the Riemann-Hurwitz relation we prove among other things the following: If g - c (resp. f - c) has at most two branches at infinity for infinitely many numbers c or if f (resp. g) is proper on the level set (resp. ), then (f,g) is bijective.
A Geometrie Approach to Keller's Jacobian Conjecture.
A local characterization of Prüfer rings.
A monogenic Hasse-Arf theorem
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
A natural map from the ext Künneth sequence to the Tor one.
A new characterization of rational surface singularities.
A Note on a Paper by Miyazaki.
A note on formal groups and zeta functions.
A note on formal power series
In this note we investigate a relationship between the boundary behavior of power series and the composition of formal power series. In particular, we prove that the composition domain of a formal power series is convex and balanced which implies that the subset consisting of formal power series which can be composed by a formal power series possesses such properties. We also provide a necessary and sufficient condition for the superposition operator to map into itself or to map into...
A note on indecomposable modules over valuation domains
A note on power invariant rings.