Application des variables non commutatives à divers produits de séries formelles
Applications of epigroups to graded ring theory.
Applying the density theorem for derivations to range inclusion problems
The problem of when derivations (and their powers) have the range in the Jacobson radical is considered. The proofs are based on the density theorem for derivations.
Approximation durch Polynomfunktionen auf universellen Algebren.
Archimedean property of ordered semirings.
Arens regularity of lattice-ordered rings
This work discusses the problem of Arens regularity of a lattice-ordered ring. In this prospect, a counterexample is furnished to show that without extra conditions, a lattice-ordered ring need not be Arens regular. However, as shown in this paper, it turns out that any -ring in the sense of Birkhoff and Pierce is Arens regular. This result is then used and extended to the more general setting of almost -rings introduced again by Birkhoff.
A-Rings
A ring R is called an E-ring if every endomorphism of R⁺, the additive group of R, is multiplication on the left by an element of R. This is a well known notion in the theory of abelian groups. We want to change the "E" as in endomorphisms to an "A" as in automorphisms: We define a ring to be an A-ring if every automorphism of R⁺ is multiplication on the left by some element of R. We show that many torsion-free finite rank (tffr) A-rings are actually E-rings. While we have an example of a mixed...
Artin-Schelter regular algebras of dimension five
We show that there are exactly three types of Hilbert series of Artin-Schelter regular algebras of dimension five with two generators. One of these cases (the most extreme) may not be realized by an enveloping algebra of a graded Lie algebra. This is a new phenomenon compared to lower dimensions, where all resolution types may be realized by such enveloping algebras.
Associated prime ideals of skew polynomial rings.
Automorphism group of representation ring of the weak Hopf algebra
Let be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra based on , then we investigate the structure of the representation ring of . Finally, we prove that the automorphism group of is just isomorphic to , where is the dihedral group with order 12.
Automorphism liftable modules
We introduce the notion of an automorphism liftable module and give a characterization to it. We prove that category equivalence preserves automorphism liftable. Furthermore, we characterize semisimple rings, perfect rings, hereditary rings and quasi-Frobenius rings by properties of automorphism liftable modules. Also, we study automorphism liftable modules with summand sum property (SSP) and summand intersection property (SIP).
Automorphismen und Antiautomorphismen von Tensoralgebren.
Automorphismes de certains completés du corps de Weyl quantique.
Automorphisms and f-simplicity in skew polynomial rings
Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings
Let be a prime ring of characteristic different from 2, its right Martindale quotient ring and its extended centroid. Suppose that , are generalized skew derivations of with the same associated automorphism , and is a non-central polynomial over such that for all . Then there exists such that for all .
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.
Automorphisms of free nilpotent associative algebras.
Automorphisms of Representation Finite Algebras.
Azumaya algebras of a ring with a finite automorphism group.