Finite dimensional divisions subalgebras of skew field coproduct

1985 ◽  
pp. 143-165
Keyword(s):  
Skew Field ◽  
Finite Dimensional

Localization in enveloping algebras

1983 ◽  
Vol 93 (3) ◽  
pp. 467-475 ◽  
Author(s):  
A. I. Lichtman
Keyword(s):  
Lie Algebra ◽  
Skew Field ◽  
Enveloping Algebras ◽  
Finite Dimensional ◽  
Noetherian Domain ◽  
Term Field

Let L be a finite-dimensional Lie algebra and U(L) its universal envelope. It is known that U(L) is a Noetherian domain (see (5), theorem v. 3·4) and therefore U(L) has a field of fractions. (Throughout the paper we use the term ‘field’ in the sense of skew field.) We prove in this article the following theorem.

The word problem for free fields: a correction and an addendum

1975 ◽  
Vol 40 (1) ◽  
pp. 69-74 ◽  
Author(s):  
P. M. Cohn
Keyword(s):  
Word Problem ◽  
Free Field ◽  
Skew Field ◽  
Finite Dimensional ◽  
Finite Set ◽  
Free Fields

In [1] it was claimed that the word problem for free fields with infinite centre can be solved. In fact it was asserted that if K is a skew field with infinite central subfield C, then the word problem in the free field on a set X over K can be solved, relative to the word problem in K.As G. M. Bergman has pointed out (in a letter to the author), it is necessary to specify rather more precisely what type of problem we assume to be soluble for K: We must be able to decide whether or not a given finite set in K is linearly dependent over its centre. This makes it desirable to prove that the free field has a corresponding property (and not merely a soluble word problem). This is done in §2; interestingly enough it depends only on the solubility of the word problem in the free field (cf. Lemma 2 and Theorem 1′ below).Bergman also notes that the proof given in [1] does not apply when K is finite-dimensional over its centre; this oversight is rectified in §4, while §3 lifts the restriction on C (to be infinite). However, we have to assume C to be the precise centre of K, and not merely a central subfield, as claimed in [1].I am grateful to G. M. Bergman for pointing out the various inaccuracies as well as suggesting remedies.

scholarly journals Skew fields with a non-trivial generalised power central rational identity

1994 ◽  
Vol 49 (1) ◽  
pp. 85-90 ◽  
Author(s):  
Katsuo Chiba
Keyword(s):  
Positive Integer ◽  
Skew Field ◽  
Finite Dimensional ◽  
Rational Identity ◽  
Skew Fields ◽  
Power Central

Let D be a skew field with uncountable centre K. The main result in the present paper is as follows: If D satisfies a non-trivial generalised power central rational identity, then D is finite dimensional over K. As a corollary we obtain the following result. Let a be an element of D such that (a−1x−1ax)q(x) ∈ K for all x ∈ D ﹨ {0} where q(x) is a positive integer depending on x. Then a ∈ K.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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