Divisible subgroups of Brauer groups and trace forms of central simple algebras.
Duo, Bézout and distributive rings of skew power series.
Embeddings into Power Series Rings.
Extending Derivations and Endomorphisms to Skew Polynomial Rings
Extensions of Chain Rings.
Finite automata and algebraic extensions of function fields
We give an automata-theoretic description of the algebraic closure of the rational function field over a finite field , generalizing a result of Christol. The description occurs within the Hahn-Mal’cev-Neumann field of “generalized power series” over . In passing, we obtain a characterization of well-ordered sets of rational numbers whose base expansions are generated by a finite automaton, and exhibit some techniques for computing in the algebraic closure; these include an adaptation to positive...
Global Dimension of Differential Operator Rings. IV - Simple Modules.
Graded modules and their completions
Injective and projective properties of -modules
We study whether the projective and injective properties of left -modules can be implied to the special kind of left -modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.
L'algorithme inverse faible et quelques anneaux qui le possèdent
Left APP-property of formal power series rings
A ring is called a left APP-ring if the left annihilator is right -unital as an ideal of for any element . We consider left APP-property of the skew formal power series ring where is a ring automorphism of . It is shown that if is a ring satisfying descending chain condition on right annihilators then is left APP if and only if for any sequence of elements of the ideal
Linearly compact chain rings.
Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings
Let be a ring. We recall that is called a near pseudo-valuation ring if every minimal prime ideal of is strongly prime. Let now be an automorphism of and a -derivation of . Then is said to be an almost -divided ring if every minimal prime ideal of is -divided. Let be a Noetherian ring which is also an algebra over ( is the field of rational numbers). Let be an automorphism of such that is a -ring and a -derivation of such that for all . Further, if for any...
Near-rings generated by -modules.
Notes on slender prime rings
If is a prime ring such that is not completely reducible and the additive group is not complete, then is slender.
On automorphism group of free quadratic extensions over a ring.
On free ring extensions of degree n.
On generalized formal power series
On -Noetherian rings
Let be a commutative ring and a given multiplicative set. Let be a strictly ordered monoid satisfying the condition that for every . Then it is shown, under some additional conditions, that the generalized power series ring is -Noetherian if and only if is -Noetherian and is finitely generated.
On the maximal condition in formal power series rings