205 research outputs found
Euclidean Quadratic Forms and ADC Forms I
Motivated by classical results of Aubry, Davenport and Cassels, we define the
notion of a Euclidean quadratic form over a normed integral domain and an ADC
form over an integral domain. The aforementioned classical results generalize
to: Euclidean forms are ADC forms. We then initiate the study and
classification of these two classes of quadratic forms, especially over
discrete valuation rings and Hasse domains.Comment: 26 page
Covering Numbers in Linear Algebra
We compute the minimal cardinality of a covering (resp. an irredundant
covering) of a vector space over an arbitrary field by proper linear subspaces.
Analogues for affine linear subspaces are also given.Comment: 4 page
- …