Extension of Zelazko’s theorem to n-Jordan homomorphisms

2019 ◽  
Vol 10 (2) ◽  
pp. 165-170 ◽  
Author(s):  
Abasalt Bodaghi ◽  
Hülya İnceboz
Keyword(s):  
Extra Condition ◽  
Jordan Homomorphisms

Abstract In this article, we correct the proof of the main theorem of Gordji’s paper [M. Eshaghi Gordji, n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 2009, 1, 159–164] by a different method and generalize Zelazko’s theorem to 4-Jordan homomorphisms by considering an extra condition.

scholarly journals Retraction of the paper entitled “Lepton number violation in a unified framework“

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Apriadi Salim Adam ◽  
Yuta Kawamura ◽  
Yamato Matsuo ◽  
Takuya Morozumi ◽  
Yusuke Shimizu ◽  
...  
Keyword(s):  
Mass Function ◽  
Lepton Number ◽  
Primordial Black Hole ◽  
Unified Framework ◽  
Extra Condition ◽  
Formal Expression ◽  
Lepton Number Violation ◽  
Standard Criterion ◽  
New Criterion ◽  
New Formula

Abstract Computations of the primordial black hole (PBH) mass function discussed in the literature have conceptual issues. They stem from the fact that the mass function is a differential quantity and the standard criterion of the PBH formation from the seed primordial fluctuations cannot be directly applied to the computation of the differential quantities. We propose a new criterion of the PBH formation, which is the addition of one extra condition to the existing one. By doing this, we derive a formal expression of the PBH mass function without introducing any ambiguous interpretations that exist in the previous studies. Once the underlying primordial fluctuations are specified, the PBH mass function can be in principle determined by the new formula. As a demonstration of our formulation, we compute the PBH mass function analytically for the case where the perturbations are Gaussian and the space is 1 dimension.

A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras

2018 ◽  
Vol 11 (02) ◽  
pp. 1850021 ◽  
Author(s):  
A. Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms ◽  
Unital Banach Algebra

We prove that each surjective Jordan homomorphism from a Banach algebra [Formula: see text] onto a semiprime commutative Banach algebra [Formula: see text] is a homomorphism, and each 5-Jordan homomorphism from a unital Banach algebra [Formula: see text] into a semisimple commutative Banach algebra [Formula: see text] is a 5-homomorphism.

scholarly journals Infinitely many equivalent versions of the graceful tree conjecture

2015 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Tao-Ming Wang ◽  
Cheng-Chang Yang ◽  
Lih-Hsing Hsu ◽  
Eddie Cheng
Keyword(s):  
Perfect Matching ◽  
Absolute Difference ◽  
Extra Condition ◽  
Graceful Labeling ◽  
The Absolute

A graceful labeling of a graph with q edges is a labeling of its vertices using the integers in [0, q], such that no two vertices are assigned the same label and each edge is uniquely identified by the absolute difference between the labels of its endpoints. The well known Graceful Tree Conjecture (GTC) states that all trees are graceful, and it remains open. It was proved in 1999 by Broersma and Hoede that there is an equivalent conjecture for GTC stating that all trees containing a perfect matching are strongly graceful (graceful with an extra condition). In this paper we extend the above result by showing that there exist infinitely many equivalent versions of the GTC. Moreover we verify these infinitely many equivalent conjectures of GTC for trees of diameter at most 7. Among others we are also able to identify new graceful trees and in particular generalize the ?-construction of Stanton-Zarnke (and later Koh- Rogers-Tan) for building graceful trees through two smaller given graceful trees.

Jordan homomorphisms of the structural matrix algebras

2015 ◽  
Vol 63 (12) ◽  
pp. 2518-2525 ◽  
Author(s):  
E. Akkurt ◽  
M. Akkurt ◽  
G.P. Barker
Keyword(s):  
Matrix Algebras ◽  
Jordan Homomorphisms ◽  
Structural Matrix

Approximate Ternary Jordan Homomorphisms on Banach Ternary Algebras

2012 ◽  
pp. 305-315
Author(s):  
Madjid Eshaghi Gordji ◽  
N. Ghobadipour ◽  
A. Ebadian ◽  
M. Bavand Savadkouhi ◽  
Choonkil Park
Keyword(s):  
Ternary Algebras ◽  
Jordan Homomorphisms

scholarly journals Characterization of $n$-Jordan Homomorphisms on Rings

2021 ◽  
Vol 53 ◽  
Author(s):  
Abbas Zivari-kazempour ◽  
Mohammad Valaei
Keyword(s):  
Jordan Homomorphism ◽  
Jordan Homomorphisms

In this paper, we prove that if $\varphi:\mathcal{R}\longrightarrow\mathcal{R}'$ is an $n$-Jordan homomorphism, where $\mathcal{R}$ has a unit $e$, then the map $a\longmapsto \varphi(e)^{n-2}\varphi(a)$ is a Jordan homomorphism.  As a consequence we show, under special hypotheses, that each $n$-Jordan homomorphism is an $n$-homomorphism.

scholarly journals Relative injectivity and CS-modules

1994 ◽  
Vol 17 (4) ◽  
pp. 661-666
Author(s):  
Mahmoud Ahmed Kamal
Keyword(s):  
Direct Decomposition ◽  
Injective Hull ◽  
Extra Condition ◽  
Direct Sums ◽  
Direct Sum ◽  
Injective Modules ◽  
Semisimple Module ◽  
Continuous Module

In this paper we show that a direct decomposition of modulesM⊕N, withNhomologically independent to the injective hull ofM, is a CS-module if and only ifNis injective relative toMand both ofMandNare CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for quasi-injective modules. But when we confine ourselves to CS-modules we need no conditions on their socles. Then we investigate direct sums of CS-modules which are pairwise relatively inective. We show that every finite direct sum of such modules is a CS-module. This result is known for quasi-continuous modules. For the case of infinite direct sums, one has to add an extra condition. Finally, we briefly discuss modules in which every two direct summands are relatively inective.

Approximations of ternary Jordan homomorphisms and derivations in multi-C ∗ ternary algebras

2011 ◽  
Vol 134 (1-2) ◽  
pp. 99-114 ◽  
Author(s):  
Donal O’Regan ◽  
John Michael Rassias ◽  
Reza Saadati
Keyword(s):  
Ternary Algebras ◽  
Jordan Homomorphisms
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