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A criterion for rings which are locally valuation rings

Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi (2009)

Colloquium Mathematicae

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 generalization of semiflows on monomials

Hamid Kulosman, Alica Miller (2012)

Mathematica Bohemica

Let K be a field, A = K [ X 1 , ⋯ , X n ] and 𝕄 the set of monomials of A . It is well known that the set of monomial ideals of A is in a bijective correspondence with the set of all subsemiflows of the 𝕄 -semiflow 𝕄 . We generalize this to the case of term ideals of A = R [ X 1 , ⋯ , X n ] , where R is a commutative Noetherian ring. A term ideal of A is an ideal of A generated by a family of terms c X 1 μ 1 ⋯ X n μ n , where c ∈ R and μ 1 , ⋯ , μ n are integers ≥ 0 .

A geometric approach to the Jacobian Conjecture in ℂ²

Ludwik M. Drużkowski (1991)

Annales Polonici Mathematici

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 g - 1 ( 0 ) (resp. f - 1 ( 0 ) ), then (f,g) is bijective.

A monogenic Hasse-Arf theorem

James Borger (2004)

Journal de Théorie des Nombres de Bordeaux

I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.

A note on formal power series

Xiao-Xiong Gan, Dariusz Bugajewski (2010)

Commentationes Mathematicae Universitatis Carolinae

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 g is convex and balanced which implies that the subset 𝕏 ¯ g consisting of formal power series which can be composed by a formal power series g possesses such properties. We also provide a necessary and sufficient condition for the superposition operator T g to map 𝕏 ¯ g into itself or to map 𝕏 g into...

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