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Dergiler / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 11 Special Issue

Abstract Omega Algebra that Subsumes Tropical Min and Max Plus Algebras

Syed Khalid Nauman(King Abdulaziz University)0000-0002-5668-7871
Cenap Özel(King Abdulaziz University)0000-0001-9673-8875
Hanifa Zekraoui(Larbi Ben M'hidi University)0000-0003-1594-5958
Sayfa
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Yayın Tarihi
2019-12-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

As applications, symmetrized omega algebras are constructed and matrices with basic operations and some topological distances over them are defined.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper abstract omega algebra is introduced and the definition is modeled in such a way that it subsumes almost all so called tropical min and max plus algebras.
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Temel Bulgular & Veri:Concrete examples of distinct nature of these algebras are presented.
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Sonuç & Katkı:As applications, symmetrized omega algebras are constructed and matrices with basic operations and some topological distances over them are defined.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Tropical geometry · idemptent semirings · max and min plus algebras

Abstract

In this paper abstract omega algebra is introduced and the definition is modeled in such a way that it subsumes almost all so called tropical min and max plus algebras. Concrete examples of distinct nature of these algebras are presented. As applications, symmetrized omega algebras are constructed and matrices with basic operations and some topological distances over them are defined.

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Bu Makaleye Atıf Yap

Nauman, S. K., Özel, C., Zekraoui, H. (2019). Abstract Omega Algebra that Subsumes Tropical Min and Max Plus Algebras. Turkish Journal of Mathematics and Computer Science, Volume: 11 Special Issue. https://ajindex.com/articles/1324864

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Kaynakça (7)

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  2. Litvinov, G.L., {\em The Maslov dequantization, idempotent and tropical mathematics: a brief introduction}, Journal of Mathematical Sciences, \textbf{140}(2007), 426--444.
  3. Maclagan, D., Sturmfels, B., Introduction to Tropical Geometry, Graduate Studies in Mathematics, Vol 161, American Mathematical Society, 2015.
  4. Ozel, C., Piekosz, A., Wajch, E., Zekraoui, H., {\em The minimizing vector theorem in symmetrized max-plus algebra}, Journal of convex analysis, \textbf{26(2)}(2019), 661--686.
  5. Pin, J. E., Tropical Semirings, Idempotency (Bristol, 1994), 50--69, Publ. Newton Inst., Vol. 11, Cambridge Univ. Press, Cambridge, 1998.
  6. Simon, I., {\em Recognizable sets with multiplicities in the tropical semiring}, pages 107--120 in Mathematical Foundations of Computer Science (Carlsbad, 1988), Lecture Notes in Computer Science, Vol. 324, Springer, Berlin, 1988.
  7. Swierczkowski, S., {\em On cyclically ordered groups}, Fundamenta Mathematicae, \textbf{47}(1959) 161--166.