scholarly journals Existentially closed Leibniz algebras and an embedding theorem

2021 ◽  
Vol 29 (2) ◽  
pp. 163-170
Author(s):  
Chia Zargeh
Keyword(s):  
Embedding Theorem ◽  
Leibniz Algebras ◽  
Existentially Closed ◽  
Hnn Extensions

Abstract In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.

scholarly journals HNN-extensions of algebras and applications

1984 ◽  
Vol 29 (2) ◽  
pp. 215-229
Author(s):  
Hans-Christian Mez
Keyword(s):  
Conjugacy Class ◽  
Additional Condition ◽  
Main Part ◽  
Regular Ring ◽  
Embedding Theorem ◽  
Closed Group ◽  
Existentially Closed ◽  
Hnn Extensions ◽  
Associative Rings ◽  
Order Sequence

The classic HNN-embedding theorem for groups does not transfer to associative rings or algebras. In its first part this paper presents constructions which provide such a theorem if an additional condition is put on the isomorphic subalgebras or if one restricts to algebras over fields and drops the associativity. The main part of the paper deals with applications of these results. For example, it is known that every existentially closed group is ω-homogeneous. It is shown that the corresponding is false for existentially closed associative Δ-algebras but true for existentially universal nonassociative K-algebras. Further-more, orthogonal sequences of idempotents in existentially closed associative Δ-algebras over a regular ring Δ are investigated. It is shown that the conjugacy class of such a sequence depends only on a corresponding order sequence. In particular, in every existentially closed K-algebra all idempotents different from 0 and 1 are conjugated.

HNN-extensions of Leibniz algebras

2019 ◽  
Vol 532 ◽  
pp. 183-200 ◽  
Author(s):  
Manuel Ladra ◽  
Mohammad Shahryari ◽  
Chia Zargeh
Keyword(s):  
Leibniz Algebras ◽  
Hnn Extensions

scholarly journals Gröbner-Shirshov Bases for Some One-relator Groups

2012 ◽  
Vol 19 (01) ◽  
pp. 99-116 ◽  
Author(s):  
Yuqun Chen ◽  
Chanyan Zhong
Keyword(s):  
Normal Form ◽  
Embedding Theorem ◽  
Hnn Extensions ◽  
Standard Normal ◽  
One Relator Groups

In this paper, we prove that two-generator one-relator groups with depth less than or equal to 3 can be effectively embedded into a tower of HNN-extensions in which each group has the effective standard normal form. We give an example to show how to deal with some general cases for one-relator groups. By using the Magnus method and Composition-Diamond Lemma, we reprove the Higman-Neumann-Neumann embedding theorem.

On solvable Leibniz algebras whose nilradical has characteristic sequence (m1,m2,m3)

2018 ◽  
Vol 2018 (3) ◽  
pp. 4-17
Author(s):  
K.K. Abdurasulov ◽  
Drew Horton ◽  
U.X. Mamadaliyev
Keyword(s):  
Characteristic Sequence ◽  
Leibniz Algebras

Existentially closed central extensions of locally finite p-groups

1986 ◽  
Vol 100 (2) ◽  
pp. 281-301 ◽  
Author(s):  
Felix Leinen ◽  
Richard E. Phillips
Keyword(s):  
Central Extensions ◽  
Locally Finite ◽  
Existentially Closed ◽  
Image Position

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.

scholarly journals Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Changbao Pang ◽  
Antti Perälä ◽  
Maofa Wang
Keyword(s):  
Borel Measure ◽  
Bergman Spaces ◽  
Embedding Theorem ◽  
Weighted Bergman Spaces ◽  
Embedding Theorems ◽  
Positive Borel Measure ◽  
Doubling Property ◽  
Area Operator ◽  
Special Cases ◽  
Upper Half Plane

AbstractWe establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$ d ω ( y ) d x with the doubling property $$\omega (0,2t)\le C\omega (0,t)$$ ω ( 0 , 2 t ) ≤ C ω ( 0 , t ) . The characterization is given in terms of Carleson squares on the upper half-plane. As special cases, our result covers the standard weights and logarithmic weights. As an application, we also establish the boundedness of the area operator.

scholarly journals The residual finiteness of HNN-extensions and generalized free products of nilpotent groups: a characterization

1992 ◽  
Vol 53 (3) ◽  
pp. 408-420 ◽  
Author(s):  
E. Raptis ◽  
D. Varsos
Keyword(s):  
Nilpotent Groups ◽  
Residual Finiteness ◽  
Finitely Generated ◽  
Free Products ◽  
Hnn Extensions ◽  
Base Group ◽  
Generalized Free Products

AbstractWe study the residual finiteness of free products with amalgamations and HNN-extensions of finitely generated nilpotent groups. We give a characterization in terms of certain conditions satisfied by the associated subgroups. In particular the residual finiteness of these groups implies the possibility of extending the isomorphism of the associated subgroups to an isomorphism of their isolated closures in suitable overgroups of the factors (or the base group in case of HNN-extensions).

scholarly journals Naturally Graded 2-Filiform Leibniz Algebras

2010 ◽  
Vol 38 (10) ◽  
pp. 3671-3685 ◽  
Author(s):  
L. M. Camacho ◽  
J. R. Gómez ◽  
A. J. González ◽  
B. A. Omirov
Keyword(s):  
Leibniz Algebras
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