Remarks on commutative noetherian rings whose flat modules have flat injective envelopes
Remarks on Henselian rings.
Remarks on iteration of formal automorphisms.
Remarks on Noetherian local domains of dim 2.
Remarks on the Cayley-van der Waerden-Chow form.
Residue class rings of real-analytic and entire functions
Let 𝓐(ℝ) and 𝓔(ℝ) denote respectively the ring of analytic and real entire functions in one variable. It is shown that if 𝔪 is a maximal ideal of 𝓐(ℝ), then 𝓐(ℝ)/𝔪 is isomorphic either to the reals or a real closed field that is an η₁-set, while if 𝔪 is a maximal ideal of 𝓔(ℝ), then 𝓔(ℝ)/𝔪 is isomorphic to one of the latter two fields or to the field of complex numbers. Moreover, we study the residue class rings of prime ideals of these rings and their Krull dimensions. Use is made of...
Resolutions by mapping cones.
Résultats récents sur l'approximation des morphismes en algèbre commutative
Révêtements étales
Ring extensions with some finiteness conditions on the set of intermediate rings
A ring extension is said to be FO if it has only finitely many intermediate rings. is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily a normal pair...
Rings generalized by tripotents and nilpotents
We present new characterizations of the rings for which every element is a sum of two tripotents and a nilpotent that commute. These extend the results of Z. L. Ying, M. T. Koşan, Y. Zhou (2016) and Y. Zhou (2018).
Rings with approximation property.
Root closure in commutative rings
Self-dual normal bases for infinite odd abelian Galois ring extensions
Semifields and a theorem of Abhyankar
Abhyankar proved that every field of finite transcendence degree over or over a finite field is a homomorphic image of a subring of the ring of polynomials (for some depending on the field). We conjecture that his result cannot be substantially strengthened and show that our conjecture implies a well-known conjecture on the additive idempotence of semifields that are finitely generated as semirings.
Separable -free modules with almost trivial dual
An -module has an almost trivial dual if there are no epimorphisms from to the free -module of countable infinite rank . For every natural number , we construct arbitrarily large separable -free -modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.
Sequences between d-sequences and sequences of linear type
The notion of a d-sequence in Commutative Algebra was introduced by Craig Huneke, while the notion of a sequence of linear type was introduced by Douglas Costa. Both types of sequences generate ideals of linear type. In this paper we study another type of sequences, that we call c-sequences. They also generate ideals of linear type. We show that c-sequences are in between d-sequences and sequences of linear type and that the initial subsequences of c-sequences are c-sequences. Finally we prove a...
Simple birational extensions of two dimensional affine rational domains
Simple Flat Extensions. II.
Simple Galois extensions of two-dimensional affine rational domains