Published March 15, 2021 | Version v1
Publication Metadata-only

A NOTE ON COMMUTATIVITY OF PRIME NEAR RING WITH GENERALIZED β-DERIVATION

Creators

  • 1. Khwaja Fareed University of Engineering and Information Technology

Description

In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a prime near ring. If there exist and two sided generalized β-derivation G associated with the non-zero two sided β-derivation on M, where is a homomorphism, satisfying the following conditions: G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) ∀ p_1,q_1 ϵ M G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) ∀ p_1,q_1 ϵ M Then M is a commutative ring.

⚠️ This is an automatic machine translation with an accuracy of 90-95%

Translated Description (Arabic)

في هذه الورقة، نثبت تبادلية الحلقات القريبة الأولية باستخدام مفهوم اشتقاقات β. لتكن M حلقة رئيسية قريبة. في حالة وجود اشتقاق β معمم من جانبين مرتبط بالاشتقاق〖 β〗 غير الصفري على الوجهين على M، حيث يوجد تجانس،〗 يستوفي الشروط التالية: G ([〖p _1,q _1 ])= p〖 _1〗 ^( u _1 )[ β(p _1 )〖,β(q _1)] p _1〗 ^( v _1)

Translated Description (French)

Dans cet article, nous prouvons la commutativité des anneaux proches premiers en utilisant la notion de dérivations β. Soit M un nombre premier proche de l'anneau. S'il existe une β-dérivation généralisée bilatérale G associée à la β-dérivation bilatérale non nulle sur M, où est un homomorphisme, satisfaisant aux conditions suivantes : G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) | p_1,q_1 | M G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) | p_1,q_1 | M Alors M est un anneau commutatif.

Translated Description (Spanish)

En este artículo, demostramos la conmutatividad de los anillos cercanos primos utilizando la noción de β-derivaciones. Deja que M sea un anillo cercano primo. Si existe una β-derivación generalizada bilateral G asociada con la β-derivación bilateral distinta de cero en M, donde es un homomorfismo, que satisface las siguientes condiciones: G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) ∀ p_1,q_1 M G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) ∀ p_1,q_1 M Entonces M es un anillo conmutativo.

Additional details

Additional titles

Translated title (Arabic)
ملاحظة حول تجميع الحلقة القريبة الرئيسية مع الاشتقاق بيتا المعمم
Translated title (French)
Une NOTE sur LA COMMUTATIVITE DE L'ANNEAU PROCHE PRIME A DERIVATION Β GENERALISEE
Translated title (Spanish)
Una NOTA sobre LA COMUTATIVIDAD DEL ANILLO CERCANO PRIMO CON Β-DERIVACIÓN GENERALIZADA

Identifiers

Other
https://openalex.org/W4211191668
DOI
10.26480/msmk.01.2021.16.19

Is supplement to
https://openalex.org/W4308298797 (Other)
https://openalex.org/W4255963200 (Other)
https://openalex.org/W3215024235 (Other)
https://openalex.org/W2949262605 (Other)
https://openalex.org/W2948782938 (Other)
https://openalex.org/W2800328333 (Other)
https://openalex.org/W2726937915 (Other)
https://openalex.org/W2599958490 (Other)
https://openalex.org/W2360590989 (Other)
https://openalex.org/W1992748119 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
Pakistan