Search results for "Finitely-generated abelian group"

GEOMETRIC EQUIVALENCE OF ALGEBRAS

2001

In this paper, we study the geometric equivalence of algebras in several varieties of algebras. We solve some of the problems formulated in [2], in particular, that of geometric equivalence for real-closed fields and finitely generated commutative groups.

Sui gruppi unitari finitari e sulla congettura di dieudonné

1996

In this paper we consider some questions concerning unitary spaces (V, h), even though (V, h) is not finitely generated.

Metric properties of the group of area preserving diffeomorphisms

2001

Area preserving cliffeoinorpliisms of the 2-disk which are identity near the boundary form a group D2 wllich can be equipped, usin-g tlhe L2nlorm on its Lie algebra, with a right invariant metric. Witll tllis metric the diameter of D2 is infinite. In this paper we sl-iow that D2 contains quasiisometric embeddings of any finitely generated free group and any finitely generated abelian free group.

On James Hyde's example of non-orderable subgroup of $\mathrm{Homeo}(D,\partial D)$

2020

In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup of $\mathrm{Homeo}(D,\partial D)$, the group of homeomorphisms of the disk fixing the boundary. This implies that the group $\mathrm{Homeo}(D,\partial D)$ itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.

Asymptotics for the multiplicities in the cocharacters of some PI-algebras

2003

We consider associative PI-algebras over a field of characteristic zero. We study the asymptotic behavior of the sequence of multiplicities of the cocharacters for some significant classes of algebras. We also give a characterization of finitely generated algebras for which this behavior is linear or quadratic.

Commutator Laws in Finitely Generated Quasivarieties

2015

Finitely Generated PI-Superalgebras with Bounded Multiplicities of the Cocharacters

2005

ABSTRACT In this note, we characterize finitely generated superalgebras satisfying an ordinary polynomial identity whose multiplicities of the supercocharacters are bounded by a constant.

On Codimension Growth of Finitely Generated Associative Algebras

1998

Abstract LetAbe a PI-algebra over a fieldF. We study the asymptotic behavior of the sequence of codimensionscn(A) ofA. We show that ifAis finitely generated overFthenInv(A)=limn→∞  c n (A) always exists and is an integer. We also obtain the following characterization of simple algebras:Ais finite dimensional central simple overFif and only ifInv(A)=dim=A.

Partial Finitely Generated Bi-Ideals

2016

Partial words have been studied by Blanchet-Sadri et al., but bi-ideals or reccurrent words have been studied for centuries by many researchers. This paper gives a solution for some problems for partial reccurrent words. This paper gives an algorithm for a given finitely generated bi-ideal, how to construct a new basis of ultimately finitely generated bi-ideal, which generates the same given bi-ideal. The paper states that it is always possible to find a basis for a given finitely generated bi-ideal. The main results of this paper are presented in third section. At first, we show that if two irreduciable bi-ideals are different, they will differ in infinitely many places. This led to the st…

Generalised power series solutions of sub-analytic differential equations

2006

Abstract We show that if a solution y ( x ) of a sub-analytic differential equation admits an asymptotic expansion ∑ i = 1 ∞ c i x μ i , μ i ∈ R + , then the exponents μ i belong to a finitely generated semi-group of R + . We deduce a similar result for the components of non-oscillating trajectories of real analytic vector fields in dimension n. To cite this article: M. Matusinski, J.-P. Rolin, C. R. Acad. Sci. Paris, Ser. I 342 (2006).