Published November 19, 2021 | Version v1
Publication Open

On Neutrosophic Quadruple Groups

Creators

  • 1. Gallup Indian Medical Center
  • 2. University of New Mexico
  • 3. Payame Noor University
  • 4. Federal University of Agriculture
  • 5. Gyeongsang National University
  • 6. Shahid Beheshti University
  • 7. Yazd University
  • 8. Shahid Bahonar University of Kerman
  • 9. University of the Punjab

Description

Abstract As generalizations and alternatives of classical algebraic structures there have been introduced in 2019 the NeutroAlgebraic structures (or NeutroAlgebras) and AntiAlgebraic structures (or AntiAlgebras). Unlike the classical algebraic structures, where all operations are well defined and all axioms are totally true, in NeutroAlgebras and AntiAlgebras, the operations may be partially well defined and the axioms partially true or, respectively, totally outer-defined and the axioms totally false. These NeutroAlgebras and AntiAlgebras form a new field of research, which is inspired from our real world. In this paper, we study neutrosophic quadruple algebraic structures and NeutroQuadrupleAlgebraicStructures. NeutroQuadrupleGroup is studied in particular and several examples are provided. It is shown that $$(NQ({\mathbb {Z}}),\div )$$ ( N Q ( Z ) , ÷ ) is a NeutroQuadrupleGroup. Substructures of NeutroQuadrupleGroups are also presented with examples.

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

Translated Description (Arabic)

الخلاصة كتعميمات وبدائل للهياكل الجبرية الكلاسيكية، تم تقديم الهياكل الجبرية المحايدة (أو NeutroAlgebras) والهياكل الجبرية المضادة (أو AntiAlgebras) في عام 2019. على عكس التراكيب الجبرية الكلاسيكية، حيث تكون جميع العمليات محددة جيدًا وجميع البديهيات صحيحة تمامًا، في NeutroAlgebras و AntiAlgebras، قد تكون العمليات محددة بشكل جيد جزئيًا والبديهيات صحيحة جزئيًا أو، على التوالي، محددة بشكل خارجي تمامًا والبديهيات خاطئة تمامًا. تشكل هذه الجبر النيوتروني والجبر المضاد مجالًا جديدًا للبحث، مستوحى من عالمنا الحقيقي. في هذه الورقة، ندرس التراكيب الجبرية الرباعية النيوتروسوفية و NeutroQuadrupleAlgebraicStructures. تتم دراسة NeutroQuadrupleGroup على وجه الخصوص ويتم تقديم العديد من الأمثلة. يتضح أن $$( NQ ({\mathbb {Z}}),\div )$$( NQ ( Z ) , ÷) هي مجموعة NeutroQuadrupleGroup. كما يتم تقديم البنى التحتية لمجموعات NeutroQuadrupleGroups مع أمثلة.

Translated Description (English)

Abstract As generalizations and alternatives of classical algebraic structures there have been introduced in 2019 the NeutroAlgebraic structures (or NeutroAlgebras) and AntiAlgebraic structures (or AntiAlgebras). Unlike the classical algebraic structures, where all operations are well defined and all axioms are totally true, in NeutroAlgebras and AntiAlgebras, the operations may be partially well defined and the axioms partially true or, respectively, totally outer-defined and the axioms totally false. These NeutroAlgebras and AntiAlgebras form a new field of research, which is inspired from our real world. In this paper, we study neutrosophic quadruple algebraic structures and NeutroQuadrupleAlgebraicStructures. NeutroQuadrupleGroup is studied in particular and several examples are provided. It is shown that $$(NQ({\mathbb {Z}}),\div )$$ ( N Q ( Z ) , ÷ ) is a NeutroQuadrupleGroup. Substructures of NeutroQuadrupleGroups are also presented with examples.

Translated Description (Spanish)

Abstract As generalizations and alternative of classical algebraic structures there have been introduced in 2019 the NeutroAlgebraic structures (or NeutroAlgebras) and AntiAlgebraic structures (or AntiAlgebras). Unlike the classical algebraic structures, where all operations are well defined and all axioms are totally true, in NeutroAlgebras and AntiAlgebras, the operations may be partially well defined and the axioms partially true or, respectively, totally outer-defined and the axioms totally false. These NeutroAlgebras and AntiAlgebras form a new field of research, which is inspired from our real world. In this paper, we study neutrosophic quadruple algebraic structures and NeutroQuadrupleAlgebraicStructures. NeutroQuadrupleGroup is studied in particular and several examples are provided. It is shown that $$(NQ({\mathbb {Z}}),\div )$$ ( N Q ( Z ) , ÷ ) is a NeutroQuadrupleGroup. Substructures of NeutroQuadrupleGroups are also presentd with examples.

Files

s44196-021-00042-9.pdf.pdf

Files (1.3 MB)

⚠️ Please wait a few minutes before your translated files are ready ⚠️ Note: Some files might be protected thus translations might not work.
Name Size Download all
md5:bd6aa4c0c28b469f4dd33dddc4e042d6
1.3 MB
Preview Download

Additional details

Additional titles

Translated title (Arabic)
على المجموعات الرباعية المتعادلة
Translated title (English)
On Neutrosophic Quadruple Groups
Translated title (Spanish)
On Neutrosophic Quadruple Groups

Identifiers

Other
https://openalex.org/W4206014889
DOI
10.1007/s44196-021-00042-9

Is supplement to
https://openalex.org/W4245490552 (Other)
https://openalex.org/W3035881305 (Other)
https://openalex.org/W3002753104 (Other)
https://openalex.org/W2142036596 (Other)
https://openalex.org/W2077600819 (Other)
https://openalex.org/W2061531152 (Other)
https://openalex.org/W2042127053 (Other)
https://openalex.org/W2007980826 (Other)
https://openalex.org/W1979597421 (Other)
https://openalex.org/W1587224694 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
Nigeria

References

  • https://openalex.org/W2755766352
  • https://openalex.org/W2807995791
  • https://openalex.org/W2899349747
  • https://openalex.org/W2900612708
  • https://openalex.org/W4235294864
  • https://openalex.org/W4287814882