A free associative algebra as a free module over a Specht subalgebra.
A generalization of Ulm subgroups
A note on flat modules
A Reduction Theorem for the Primitivity of Tensor Products.
A splitting theorem for ℱ-products
Actions of the additive group on certain noncommutative deformations of the plane
We connect the theorems of Rentschler [rR68] and Dixmier [jD68] on locally nilpotent derivations and automorphisms of the polynomial ring and of the Weyl algebra , both over a field of characteristic zero, by establishing the same type of results for the family of algebras where is an arbitrary polynomial in . In the second part of the paper we consider a field of prime characteristic and study comodule algebra structures on . We also compute the Makar-Limanov invariant of absolute constants...
An embedding theorem for free associative algebras.
Approximation de séries formelles par des séries rationnelles
Arithmetical properties of finite rings and algebras, and analytic number theory. II.
Automorphisms of free nilpotent associative algebras.
Basis for identities of the algebra of simplified insertion.
Bimodule resolution of the Liu-Schulz algebras.
Composition-diamond lemma for modules
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the Verma module...
Concerning Colimits in the Category of Noncommutative Algebras
Correction to "The universal skew field of fractions of a tensor product of free rings" (Colloq. Math. 72 (1997), 1-8)
Degree estimate for subalgebras generated by two elements
We develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong...
Dually steady rings
Exact sequences for mixed coproduct/ tensor-product ring constructions.
To a commutative ring K, and a family of K-algebras indexed by the vertex set of a graph, we associate a K-algebra obtained by a mixture of coproduct and tensor product constructions. For this, and related constructions, we give exact sequences and deduce homological properties.
Extension d'un théorème de Pólya-Cantor à des séries rationnelles en variables non commutatives
Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures
First, we provide an introduction to the theory and algorithms for noncommutative Gröbner bases for ideals in free associative algebras. Second, we explain how to construct universal associative envelopes for nonassociative structures defined by multilinear operations. Third, we extend the work of Elgendy (2012) for nonassociative structures on the 2-dimensional simple associative triple system to the 4- and 6-dimensional systems.