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1
Algebra II: Chapters 4-7
T 8) Let A be a nonempty subset of a commutative field K of characteristic ^ 2 ;
then K is said to be A-orderable if no element of A is a sum of squares in K. We
say that K is orderable if there exists a total ordering of K which is compatible with
its ...
2
Open Problems in Topology II
Weak selections and orderability A space X is orderable (or linearly orderable) if
the topology of X coincides with the open interval topology on X generated by a
linear ordering on X. A space X is suborderable (or generalized ordered) if it can
...
3
Runtime Verification: 9th International Workshop, RV 2009, ...
specification TOTALORDERWITHSUC sorts Successorable < Orderable
constructors suc: Successorable −→ Successorable; axioms E, F: Successorable
; geq(suc(E) , E) ; geq(E, suc(F)) if geq(E,F) and not (E = F); E = F if suc(E) = E
and ...
Saddek Bensalem, Doron A. Peled, 2009
4
Combinatorial Geometries
It follows that M*(S) is base orderable. D 5.4.4. Corollary. Each minor of a base
orderable matroid is base orderable. Proof. This is an immediate consequence of
Lemmas 5.4.2 and 5.4.3. D 5.4.5. Proposition. A Menger matroid is a base ...
5
Groups St Andrews 2009 in Bath:
Theorem 4.7 ([7]) (iv) The Boone–Britton group in [10] is a right-orderable finitely
presented group with insoluble group word problem. (v) (cf. The Higman
Embedding Theorem) A finitely generated right-orderable group can be
embedded in a ...
C. M. Campbell, M. R. Quick, E. F. Robertson, 2011
6
Cellular Automata and Groups
(a) Every subgroup of an orderable group is orderable. Indeed, if H is a subgroup
of a group G and ≤ is a left-invariant total ordering on G, then the restriction of ≤
to H is a left-invariant total ordering on H. (b) The additive groups Z, Q, and R ...
Tullio Ceccherini-Silberstein, Michel Coornaert, 2010
7
The Theory of Lattice-Ordered Groups
(Kokorin [6].) Let G be an orderable group, H be a normal G-fully orderable
relatively convex subgroup of G. If agi+ -+sn . a-« € # for all <7i, . . . ,gn in G, then
the element a is comparable with e under every maximal partial order on G. Proof
.
V.M. Kopytov, Nikolai Yakovlevich Medvedev, 1994
8
Graph Classes: A Survey
From the definition it is obvious that Welsh- Powell and Matula perfect graphs are
perfectly orderable. Furthermore, hereditary Matula perfect graphs are HMD-free [
219]. Cochand and de Werra [228] give a forbidden induced subgraph ...
Andreas Brandstädt, Van Bang Le, Jeremy P. Spinrad, 1999
9
Skein Modules,
Orderable Magmas, and Billiards
We investigate three results in this dissertation.
10
Applied Discrete Structures
(a) the duals, the minors, and the unions of base orderable matroids are base
orderable, (b) the duals, the minors, and the unions of strongly base orderable
matroids are strongly base orderable, (c) all transversal matroids are strongly
base ...
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