Orderings and valuations in hyperfields

Orderings and Signatures of Higher Level on Multirings and Hyperfields

Multirings are objects like rings but with multi-valued addition. They are a variant of other objects called hyperrings, defined by Krasner [12], [13]. In [16] the second author defines multirings, introduces a certain special class of multirings called real reduced multirings, defines a natural reflection A Ã Qred(A) from the category of multirings satisfying −1 / ∈ ∑ A2 to the full subcategor...

Orderings and Valuations on Twisted Polynomial Rings

The real spectra of certain \twisted" polynomial algebras A over R are examined. In certain cases, including Weyl algebras and universal enveloping algebras of solvable Lie algebras, the stability indices of the residue spaces of Sper(A) are estimated. The results show that the Brr ocker-Scheiderer theory of minimal generation of constructible sets applies to Sper(A) in these cases. An attempt ...

Orderings, Valuations and Hermitian Forms over ∗-fields

Forking and Dividing in Fields with Several Orderings and Valuations

variety). For each i, let φi(x) be a C-dense quantifier-free Li-formula with parameters from K. Then we can find a K-definable rational function f : C → P which is non-constant, and has the property that the divisor f−1(0) is a sum of distinct points in ⋂n i=1 φi(K), with no multipliticities. (In particular, the support of the divisor contains no points from C(K)\C(K) and no points from C \ C.)...

∗−orderings and ∗−valuations on Algebras of Finite Gelfand-kirillov Dimension

Considerable work has been done in developing the relationship between ∗-orderings, ∗valuations and the reduced theory of Hermitian forms over a skewfield with involution [12] [13] [14] [15] [16] [23] [24]. This generalizes the well-known theory in the commutative case; e.g., see [4] [6] [7] [27]. In the commutative theory, formally real function fields provide a rich source of examples [6]. In...