arXiv subjects
Publications and source records attributed to David W. Lewis.
A categorical approach is proposed for the construction of 8-periodic chain complexes of Witt groups of categories with duality. Exactness of the resulting sequences is proved under the hypothesis that the categories are abelian and artinian or when the endomorphism algebra of each object is semilocal and rad-adically complete.
This bundle contains the paper "Hermitian Morita Theory: a Matrix Approach", published in Irish Math. Soc. Bulletin 62 (2008), pp. 37-41 (reproduced with permission of the Irish Mathematical Society), and with abstract "In this note an explicit matrix description of hermitian Morita theory is presented." and a short erratum.
In ``New Proofs of the structure theorems for Witt Rings'', Lewis shows how the standard ring-theoretic results on the Witt ring can be deduced in a quick and elementary way from the fact that the Witt ring of a field is integral and from the specific nature of the explicit annihilating polynomials he provides. We will show in the present article that the same structure results hold for larger classes of commutative rings and not only for Witt rings. We will construct annihilating polynomials for these rings.