Homological methods in the solution of certain functional equations.
On limits and colimits in the Kleisli category
A note on reflective subcategories defined by partial algebras
Generalized colorings and avoidable orientations
Gallai and Roy proved that a graph is k-colorable if and only if it has an orientation without directed paths of length k. We initiate the study of analogous characterizations for the existence of generalized graph colorings, where each color class induces a subgraph satisfying a given (hereditary) property. It is shown that a graph is partitionable into at most k independent sets and one induced matching if and only if it admits an orientation containing no subdigraph from a family of k+3 directed...
Lifting tensorproducts along non-adjoint functors
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...
Matrices over centrally -graded rings.
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