On Commutativity of Semiprime Rings with Multiplicative (Generalized)-derivations

Kumar, Deepak; Sandhu, Gurninder S.

doi:10.5539/jmr.v9n2p9

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…Thus, it would be a fact of interest to prove the results of generalized derivation for multiplicative (generalized)derivations. In this direction many results has been obtained during last five years (see [6,[12][13][14]). Recently, Tiwari et al [12] studied the following identities involving generalized derivations on some appropriate subsets of prime rings:…”

Section: Xy ϵ Z(r) Holds For All X Y ϵ I Then R Contains a Nonzero mentioning

confidence: 99%

Remarks on Derivable Maps of Semi-prime Rings

Sandhu¹,

Kumar²

2017

JCSCM

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Let R be an associative ring with center Z(R) and a nonzero ideal I. Let G and F are multiplicative (generalized)derivations of R together with mappings g and f respectively. In this note, we prove that R contains a non-zero central ideal if any one of the following holds for all x, y in I: 1. G(xy) ± F(x)F(y) ± [x,y] ϵ Z(R) 2. G(xy) ± F(x)F(y) ± (xoy) ϵ Z(R) 3. G(xy) ± F(x)F(y) ± yx ϵ Z(R) 4. G(xy) ± F(x)F(y) ± xy ϵ Z(R) Moreover, we investigate the identities F(x)F(y) ± yx ϵ Z(R) and F(xy) ± yx ϵ Z(R) over a non-zero left ideal of R and improve some known results.

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Section: Xy ϵ Z(r) Holds For All X Y ϵ I Then R Contains a Nonzero mentioning

confidence: 99%

Remarks on Derivable Maps of Semi-prime Rings

Sandhu¹,

Kumar²

2017

JCSCM

Self Cite

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“…Thus, it would be a fact of interest to prove the results of generalized derivations for multiplicative (generalized)-derivations. Recently, a number of results involving multiplicative (generalized)derivations has been obtain (see [10,14,15,18] and references therein). Tiwari et.…”

Section: Introductionmentioning

confidence: 99%

A study of derivable mappings of semiprime rings

Sandhu

Kumara

2018

Int. J. of Algeb. and Stat.

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Parameters affecting outcome of paediatric cardiomyopathies in the intensive care unit: experience of an Egyptian tertiary centre over 7 years

Sobeih

El-Saiedi

Khalek

et al. 2020

Libyan Journal of Medicine

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Introduction: Paediatric cardiomyopathies are rare but serious and often life-threatening conditions. In the absence of cardiac transplant and ventricular assist device as treatment options in our region, it is very important to identify patients at higher risk. The aim of this study was to determine the outcome of patients diagnosed with cardiomyopathies and their prognostic indicators. Patients and methods: This study included 92 cases representing all patients diagnosed with cardiomyopathy who were admitted into the pediatric cardiac intensive care unit during the period from January 2012 to September 2018. The patients were classified into two groups according to the outcome: the first group comprised 69 patients who survived, and the second group comprised 23 patients who died. All medical records were reviewed, and data were recorded and analysed. Results: Patients with cardiomyopathies represented 8.6% (92/1071) of all patients with cardiac diseases who were admitted in the study period and in the target age group (0.5-12 years). Dilated cardiomyopathy (DCM) was the most frequent type of cardiomyopathy among the admitted patients (80 patients), while 6 patients were diagnosed with hypertrophic cardiomyopathy (HCM), 4 were diagnosed with restrictive cardiomyopathy (RCM), and only 2 were diagnosed with mixed DCM-RCM. Seventy patients required inotropic support (76.1%). Assisted mechanical ventilation was used on 15 patients (16.3%). Twenty-three patients (25.0%) died during the 7-year study period. ConclusionsConclusions The occurrence of hypotension, abnormally high liver enzymes, the need for mechanical ventilation and the need for multiple inotropic drugs were found to be statistically significant predictors of mortality, while age, sex, fractional shortening, ejection fraction, presence of mitral regurgitation, mural thrombus, electrolyte disturbance and arrhythmias did not predict or affect patients' outcomes.

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On Commutativity of Semiprime Rings with Multiplicative (Generalized)-derivations

Abstract: The aim of this paper is to explore the commutativity of semiprime rings admitting multiplicative (generalized)-derivations and satisfy certain hypotheses on appropriate subsets.

Cited by 3 publications

References 16 publications

Remarks on Derivable Maps of Semi-prime Rings

Remarks on Derivable Maps of Semi-prime Rings

A study of derivable mappings of semiprime rings

Parameters affecting outcome of paediatric cardiomyopathies in the intensive care unit: experience of an Egyptian tertiary centre over 7 years

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