Cancellative relations and matrices
Carriers of torsion-free groups
Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring
2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.For an n×n matrix A over an arbitrary unitary ring R, we obtain the following Cayley-Hamilton identity with right matrix coefficients: (λ0I+C0)+A(λ1I+C1)+… +An-1(λn-1I+Cn-1)+An (n!I+Cn) = 0, where λ0+λ1x+…+λn-1 xn-1+n!xn is the right characteristic polynomial of A in R[x], I ∈ Mn(R) is the identity matrix and the entries of the n×n matrices Ci, 0 ≤ i ≤ n are in [R,R]. If R is commutative, then C0 = C1 = … = Cn-1 = Cn = 0 and our...
Centralizer near-rings acting on SE-groups.
Centralizers and the isomorphism problem for nearrings.
Characterization of matrix types of ultramatricial algebras.
Classes of modules related to Serre subcategories.
Classical quotient rings of generalized matrix rings.
Clifford theory for group-graded rings.
Clifford theory for group-graded rings. II.
Cohomology of the triangular algebra and applications. (Cohomologie de l'algèbre triangulaire et applications.)
Comments on gentleness of endomorphism algebras.
Completely O-simple multiplicative ideals of rings.
Computation of the mapping of factorization by the radical for of the endomorphism ring.
Computing homomorphism spaces between modules over finite dimensional algebras.
Construction of Auslander-Gorenstein local rings as Frobenius extensions
Starting from an arbitrary ring R we provide a systematic construction of ℤ/nℤ-graded rings A which are Frobenius extensions of R, and show that under mild assumptions, A is an Auslander-Gorenstein local ring if and only if so is R.
Corrigendum to the paper " Quotient rings and one-sided primes".
Cotorsion-free algebras as endomorphism algebras in - the discrete and topological cases
The discrete algebras over a commutative ring which can be realized as the full endomorphism algebra of a torsion-free -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...