Displaying similar documents to “An embedding theorem for commutative B 0 -algebras”

Fréchet algebras and formal power series

Graham Allan (1996)

Studia Mathematica

Similarity:

The class of elements of locally finite closed descent in a commutative Fréchet algebra is introduced. Using this notion, those commutative Fréchet algebras in which the algebra ℂ[[X]] may be embedded are completely characterized, and some applications to the theory of automatic continuity are given.

Raising bounded groups and splitting of radical extensions of commutative Banach algebras

W. Bade, P. Curtis, A. Sinclair (2000)

Studia Mathematica

Similarity:

Let A be a commutative unital Banach algebra and let A/ℛ be the quotient algebra of A modulo its radical ℛ. This paper is concerned with raising bounded groups in A/ℛ to bounded groups in the algebra A. The results will be applied to the problem of splitting radical extensions of certain Banach algebras.

Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras

K.K. Abdurasulov, A.Kh. Khudoyberdiyev, M. Ladra, A.M. Sattarov (2021)

Communications in Mathematics

Similarity:

In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly...

A note on topologically nilpotent Banach algebras

P. Dixon, V. Müller (1992)

Studia Mathematica

Similarity:

A Banach algebra A is said to be topologically nilpotent if s u p ∥ x ₁ . . . . . . x n ∥ 1 / n : x i ∈ A , ∥ x i ∥ ≤ 1 ( 1 ≤ i ≤ n ) tends to 0 as n → ∞. We continue the study of topologically nilpotent algebras which was started in [2]

On Kolchin's theorem.

Israel N. Herstein (1986)

Revista Matemática Iberoamericana

Similarity:

A well-known theorem due to Kolchin states that a semi-group G of unipotent matrices over a field F can be brought to a triangular form over the field F [4, Theorem H]. Recall that a matrix A is called unipotent if its only eigenvalue is 1, or, equivalently, if the matrix I - A is nilpotent. Many years ago I noticed that this result of Kolchin is an immediate consequence of a too-little known result due to Wedderburn [6]. This result of Wedderburn asserts that if B is a finite...

Nil series from arbitrary functions in group theory

Ian Hawthorn (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In an earlier paper distributors were defined as a measure of how close an arbitrary function between groups is to being a homomorphism. Distributors generalize commutators, hence we can use them to try to generalize anything defined in terms of commutators. In this paper we use this to define a generalization of nilpotent groups and explore its basic properties.