An Application of a Theorem of Ziegler.
An isomorphism theorem for algebras
Anneaux Corpomorphes
Anneaux semi-artiniens non commutatifs
Anneaux semi-premiers, noethériens, à identités polynômiales
Applications logiques en théorie des anneaux et des modules
Applications of Model Theory to Representations of Finite-Dimensional Algebras.
Arithmetical properties of finite rings and algebras, and analytic number theory.
Arithmetical properties of finite rings and algebras, and analytic number theory. IV. Relative asymptotic enumeration and L-series.
Assoziative Tripelsysteme.
Auslander-Reiten Quivers of local orders of finite lattice type.
Automorphismen und Antiautomorphismen von Tensoralgebren.
Automorphisms of completely primary finite rings of characteristic p
A completely primary ring is a ring R with identity 1 ≠ 0 whose subset of zero-divisors forms the unique maximal ideal . We determine the structure of the group of automorphisms Aut(R) of a completely primary finite ring R of characteristic p, such that if is the Jacobson radical of R, then ³ = (0), ² ≠ (0), the annihilator of coincides with ² and , the finite field of elements, for any prime p and any positive integer r.
Centers in domains with quadratic growth
Let F be a field, and let R be a finitely-generated F-algebra, which is a domain with quadratic growth. It is shown that either the center of R is a finitely-generated F-algebra or R satisfies a polynomial identity (is PI) or else R is algebraic over F. Let r ∈ R be not algebraic over F and let C be the centralizer of r. It is shown that either the quotient ring of C is a finitely-generated division algebra of Gelfand-Kirillov dimension 1 or R is PI.
Centres and Fixed-Point Rings of Artinian Rings.
Classification of finite rings: theory and algorithm
An interesting topic in the ring theory is the classification of finite rings. Although rings of certain orders have already been classified, a full description of all rings of a given order remains unknown. The purpose of this paper is to classify all finite rings (up to isomorphism) of a given order. In doing so, we introduce a new concept of quasi basis for certain type of modules, which is a useful computational tool for dealing with finite rings. Then, using this concept, we give structure...
Coefficient subrings of certain local rings with prime-power characteristic.
Complexity and periodicity
Let M be a finitely generated module over an Artin algebra. By considering the lengths of the modules in the minimal projective resolution of M, we obtain the Betti sequence of M. This sequence must be bounded if M is eventually periodic, but the converse fails to hold in general. We give conditions under which it holds, using techniques from Hochschild cohomology. We also provide a result which under certain conditions guarantees the existence of periodic modules. Finally, we study the case when...
Computing homomorphism spaces between modules over finite dimensional algebras.
Conjugation in semigroups and finite dimensional algebras