1,535 research outputs found
Quasi-Duo Skew Polynomial Rings
A characterization of right (left) quasi-duo skew polynomial rings of
endomorphism type and skew Laurent polynomial rings are given. In particular,
it is shown that (1) the polynomial ring R[x] is right quasi-duo iff R[x] is
commutative modulo its Jacobson radical iff R[x] is left quasi-duo, (2) the
skew Laurent polynomial ring is right quasi-duo iff it is left quasi-duo. These
extend some known results concerning a description of quasi-duo polynomial
rings and give a partial answer to the question posed by Lam and Dugas whether
right quasi-duo rings are left quasi-duo
Parameter test ideals of Cohen Macaulay rings
We describe an algorithm for computing parameter-test-ideals in certain local
Cohen-Macaulay rings. The algorithm is based on the study of a Frobenius map on
the injective hull of the residue field of the ring and on the application of
Rodney Sharp's notion of ``special ideals''.
Our techniques also provide an algorithm for computing indices of nilpotency
of Frobenius actions on top local cohomology modules of the ring and on the
injective hull of its residue field. The study of nilpotent elements on
injective hulls of residue fields also yields a great simplification of the
proof of the fact that for a power series ring of prime characteristic, for
all nonzero , generates as a -module.Comment: 16 pages To appear in Compositio Mathematic
- …