Let $$\mathcal {R}$$ be an expansion of the ordered real additive group. When is o-minimal, it known that either defines field isomorphic to $$(\mathbb {R},<,+,\cdot )$$ on some open subinterval $$I\subseteq \mathbb , or a reduct vector space. We say field-type if satisfies former condition. In this paper, we prove more general result for arbitrary expansions {R},<,+)$$ . particular, show do no...

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

A partially ordered group G = (G, +, ≤) is both a (not necessarily Abelian) group (G, +) (with binary operation + and identity element 0, where the inverse of a member a of G is denoted by −a) and a partially ordered set (G, ≤) in which a ≥ b implies that a+ c ≥ b+ c and c+ a ≥ c+ b for a, b, and c in G. An element a of G is positive if a ≥ 0. A partially ordered group (G, +, ≤) is called a lat...

We prove that for no nontrivial ordered abelian group G, the ordered power series field R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that there is a nonsurjective logarithm. For an arbitrary ordered field k, no exponential on k((G)) is compatible, that is, induces an exponential on k through t...

William W. Boone and Graham Higman proved that a finitely generated group has soluble word problem if and only if it can be embedded in a simple group that can be embedded in a finitely presented group. We prove the exact analogue for lattice-ordered groups: Theorem: A finitely generated lattice-ordered group has soluble word problem if and only if it can be `-embedded in an `-simple lattice-or...

the phenylthiourea-substituted triethoxysilane as a silane agent was synthesized and grafted on highly ordered nanoporous silica (lus-1) with a textured morphology and hexagonal array. this material (tu-lus-1) contained 0.8 mmol/g of soft base phenylthiourea group and surface area 760 m2g-1 and was able to adsorb 0.75 mmolhg/g of tu-lus-1 in endothermic reaction.

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 ...