scholarly journals Extension Property of Automorphism of Modules

2021 ◽  
Vol 67 (1) ◽  
pp. 61-71
Author(s):  
Abderrahim El Moussaouy ◽  
◽  
M’hammed Ziane ◽  
Keyword(s):  
Extension Property ◽  
Injective Module

In this paper we generalize Schupp’s result for groups to modules. For an injective module, every automorphism satisfies the extension property. We characterize the automorphisms of a module M satisfies the extension property.

scholarly journals On the c0-extension property for compact lines

2015 ◽  
Vol 428 (1) ◽  
pp. 184-193
Author(s):  
Claudia Correa ◽  
Daniel V. Tausk
Keyword(s):  
Extension Property

scholarly journals Biquasitriangularity and spectral continuity

1985 ◽  
Vol 26 (2) ◽  
pp. 177-180 ◽  
Author(s):  
Ridgley Lange
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Invariant Subspaces ◽  
Extension Property ◽  
Point Of View ◽  
Single Valued Extension Property ◽  
Continuity Theorem ◽  
Spectral Continuity ◽  
Necessary And Sufficient ◽  
Continuity Of The Spectrum

In [6] Conway and Morrell characterized those operators on Hilbert space that are points of continuity of the spectrum. They also gave necessary and sufficient conditions that a biquasitriangular operator be a point of spectral continuity. Our point of view in this note is slightly different. Given a point T of spectral continuity, we ask what can then be inferred. Several of our results deal with invariant subspaces. We also give some conditions characterizing a biquasitriangular point of spectral continuity (Theorem 3). One of these is that the operator and its adjoint both have the single-valued extension property.

Psq-injective modules and rings

2021 ◽  
pp. 2250101
Author(s):  
Avanish Kumar Chaturvedi ◽  
Sandeep Kumar
Keyword(s):  
Injective Module ◽  
Injective Modules

For any two right [Formula: see text]-modules [Formula: see text] and [Formula: see text], [Formula: see text] is said to be a ps-[Formula: see text]-injective module if, any monomorphism [Formula: see text] can be extended to [Formula: see text]. Also, [Formula: see text] is called psq-injective if [Formula: see text] is a ps-[Formula: see text]-injective module. We discuss some properties and characterizations in terms of psq-injective modules.

Property (ω) and the Single-valued Extension Property

2021 ◽  
Vol 37 (8) ◽  
pp. 1254-1266
Author(s):  
Lei Dai ◽  
Xiao Hong Cao ◽  
Qi Guo
Keyword(s):  
Extension Property ◽  
Single Valued Extension Property

scholarly journals Bipolar Fuzzy Implicative Ideals of BCK-Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
G. Muhiuddin ◽  
D. Al-Kadi
Keyword(s):  
Fuzzy Set ◽  
Extension Property ◽  
Fuzzy Ideal

The notion of bipolar fuzzy implicative ideals of a BCK-algebra is introduced, and several properties are investigated. The relation between a bipolar fuzzy ideal and a bipolar fuzzy implicative ideal is studied. Characterizations of a bipolar fuzzy implicative ideal are given. Conditions for a bipolar fuzzy set to be a bipolar fuzzy implicative ideal are provided. Extension property for a bipolar fuzzy implicative ideal is stated.

scholarly journals ON YI'S EXTENSION PROPERTY FOR TOTALLY PREORDERED TOPOLOGICAL SPACES

2006 ◽  
Vol 43 (1) ◽  
pp. 159-181 ◽  
Author(s):  
M.J. CAMPION ◽  
J.C. CANDEAL ◽  
ESTEBAN INDURAIN
Keyword(s):  
Extension Property ◽  
Topological Spaces

scholarly journals Property $(w)$ of upper triangular operator Matrices

2020 ◽  
Vol 51 (2) ◽  
pp. 81-99
Author(s):  
Mohammad M.H Rashid
Keyword(s):  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Extension Property ◽  
Operator Matrices ◽  
Single Valued Extension Property ◽  
Triangular Operator ◽  
Upper Triangular Operator Matrices ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Number Of Authors

Let $M_C=\begin{pmatrix} A & C \\ 0 & B \\ \end{pmatrix}\in\LB(\x,\y)$ be be an upper triangulate Banach spaceoperator. The relationship between the spectra of $M_C$ and $M_0,$ and theirvarious distinguished parts, has been studied by a large number of authors inthe recent past. This paper brings forth the important role played by SVEP,the {\it single-valued extension property,} in the study of some of these relations. In this work, we prove necessary and sufficient conditions of implication of the type $M_0$ satisfies property $(w)$ $\Leftrightarrow$ $M_C$ satisfies property $(w)$ to hold. Moreover, we explore certain conditions on $T\in\LB(\hh)$ and $S\in\LB(\K)$ so that the direct sum $T\oplus S$ obeys property $(w)$, where $\hh$ and $\K$ are Hilbert spaces.

scholarly journals Extension theorems for various weight functions over Frobenius bimodules

2018 ◽  
Vol 17 (03) ◽  
pp. 1850052 ◽  
Author(s):  
Heide Gluesing-Luerssen ◽  
Tefjol Pllaha
Keyword(s):  
Duality Theory ◽  
Extension Property ◽  
Finite Ring ◽  
Weight Functions ◽  
Hamming Weight ◽  
Theoretic Approach ◽  
Extension Theorems ◽  
Homogeneous Weight

In this paper, we study codes where the alphabet is a finite Frobenius bimodule over a finite ring. We discuss the extension property for various weight functions. Employing an entirely character-theoretic approach and a duality theory for partitions on Frobenius bimodules, we derive alternative proofs for the facts that the Hamming weight and the homogeneous weight satisfy the extension property. We also use the same techniques to derive the extension property for other weights, such as the Rosenbloom–Tsfasman weight.

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