Almost-ordered and ordered local rings and their geometrical application

Ordered Rings and Fields

Lattice-Ordered Rings and Function Rings

Introduction: This paper treats the structure of those lattice-ordered rings which are subdirect sums of totally ordered rings—the f-rings of Birkhoff and Pierce [4]. Broadly, it splits into two parts, concerned respectively with identical equations and with ideal structure; but there is an important overlap at the beginning. D. G. Johnson has shown [9] that not every /-ring is unitable, i.e. e...

ABSORBENT ORDERED FILTERS AND THEIR FUZZIFICATIONS IN IMPLICATIVE SEMIGROUPS

The notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. Relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. The extensionproperty for (fuzzy) absorbent orderedfilters is established. Conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

Groups definable in ordered vector spaces over ordered division rings

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G,⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex W -definable subgroup U of 〈Mn, +〉 and a lattice L of rank n. As two conseq...

Existentially closed ordered difference fields and rings

We describe classes of existentially closed ordered difference fields and rings. We show an Ax-Kochen type result for a class of valued ordered difference fields. 1. Existentially closed real-closed difference fields. In the first part of this paper we will consider on one hand difference totally ordered fields, namely totally ordered fields with a distinguished automorphism σ and on the other ...