Hall algebras and quantum groups.
Locally free modules
Monoid rings that are firs.
It is well known that the monoid ring of the free product of a free group and a free monoid over a skew field is a fir. We give a proof of this fact that is more direct than the proof in the literature.
Numérateurs et dénominateurs dans le corps de fractions d'un semifir
On a theorem of McCoy
We study McCoy’s theorem to the skew Hurwitz series ring for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring satisfies McCoy’s theorem of skew Hurwitz series.
On Filtered Modules and their Associated Graded Modules.
On presentations of semigroup rings
Siano un ideale di un anello e una congruenza su un semigruppo . Consideriamo l'anello semigruppo come un'immagine omomorfa dell'anello semigruppo . Questo è fatto in tre passi: prima studiando l'anello semigruppo , poi e infine combinando i due casi speciali. In ciascun caso, determiniamo l'ideale che è il nucleo dell'omomorfismo in questione. I risultati corrispondenti per le -algebre, dove è un anello commutativo, possono essere facilmente dedotti. Alcuni raffinamenti, casi speciali...
On rings satisfying certain polynomial identities.
On semifir monoid rings.
We give a new condition on a monoid M for the monoid ring F[M] to be a 2-fir. Furthermore, we construct a monoid M that satisfies all the currently known necessary conditions for F[M] to be a semifir and that the group of units of M is trivial, but M is not a directed union of free monoids.
On subrings of amalgamated free products of rings
The aim of this paper is to develop the homological machinery needed to study amalgams of subrings. We follow Cohn [1] and describe an amalgam of subrings in terms of reduced iterated tensor products of the rings forming the amalgam and prove a result on embeddability of amalgamated free products. Finally we characterise the commutative perfect amalgamation bases.
On the ring of the variety of algebras over a ring
Ordering Epic R-Fields
Power Series over Coherent Rings.
Primitive Derivations in Free Associative Algebras.
Progrès récent dans l'étude des algèbres associatives libres
Steady ideals and rings
Sur divers produits de séries formelles
The Automorphism Group of the Free Algebra of Rank Two
The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group...
The free -ring is a graded -ring.
The -graded identities of the Grassmann Algebra
Let be a finite abelian group with identity element and be an infinite dimensional -homogeneous vector space over a field of characteristic . Let be the Grassmann algebra generated by . It follows that is a -graded algebra. Let be odd, then we prove that in order to describe any ideal of -graded identities of it is sufficient to deal with -grading, where , and if . In the same spirit of the case odd, if is even it is sufficient to study only those -gradings such that...