Semisimplicial Unital Groups
نویسندگان
چکیده
If there is an order-preserving group isomorphism from a directed abelian group G with a finitely generated positive cone G+ onto a simplicial group, then G is called a semisimplicial group. By factoring out the torsion subgroup of a unital group having a finite unit interval, one obtains a semisimplicial unital group. We exhibit a representation for the base-normed space associated with a semisimplicial unital group G as the Banach dual space of a finite dimensional order-unit space that contains G as an additive subgroup. In terms of this representation, we formulate necessary and sufficient conditions for G to be archimedean.
منابع مشابه
(Compression Bases in Unital Groups
We introduce and launch a study of compression bases in unital groups. The family of all compressions on a compressible group and the family of all direct compressions on a unital group are examples of compression bases. In this article we show that the properties of the compatibility relation in a compressible group generalize to unital groups with compression bases. AMS Classification: Primar...
متن کاملClean Unital -groups
A ring with identity is said to be clean if every element can be written as a sum of a unit and an idempotent. The study of clean rings has been at the forefront of ring theory over the past decade. The theory of partially-ordered groups has a nice and long history and since there are several ways of relating a ring to a (unital) partially-ordered group it became apparent that there ought to be...
متن کاملClassification of Finitely Generated Lattice-ordered Abelian Groups with Order-unit
A unital l-group (G,u) is an abelian group G equipped with a translation-invariant lattice-order and a distinguished element u, called orderunit, whose positive integer multiples eventually dominate each element of G. We classify finitely generated unital l-groups by sequences W = (W0,W1, . . .) of weighted abstract simplicial complexes, where Wt+1 is obtained from Wt either by the classical Al...
متن کاملAn Algebraic Property of an Isometry between the Groups of Invertible Elements in Banach Algebras
We show that if T is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then T is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the underling algebras are closed unital standard operator algebras, (T (eA)) −1 T is extended to a surjective real algebra isomorphism; if T is a surjective isometry...
متن کاملCollineation Groups Preserving a Unital in a Projective Plane of Order
A unital embedded in a finite projective plane Π of order m# is a substructure of Π which forms a 2®(m$1,m1, 1) design. Several authors devoted their attention to the embedded unitals. The main aim is either to construct and investigate new classes of unitals, or to characterize some classes using group-theoretical or graphical properties [3, 6, 9, 18, 25]. In [3] we give some general results...
متن کامل