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Journals / Kırşehir Ahi Evran Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 2 Sayı: 1

Crossed Corner of Commutative Algebra and Moore BiComplex

Değişmeli Cebirler için Çaprazlanmış Köşe ve Moore Bikompleks

Hatice Binbir(TC MİLLİ EĞİTİM BAKANLIĞI KONYA)0009-0003-6684-5049
Özgün Gürmen Alansal(KÜTAHYA DUMLUPINAR ÜNİVERSİTESİ)0000-0003-2851-986X
Pages
12–18
Publication Date
2024-06-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

If we take NE_00={0}, we have proved that the new structure obtained forms a crossed corner structure.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A simplicial algebra models algebraic structures that correspond to homotopy types.
📊
Key Findings & Data:In this regard, simplicial algebras with a dimension of Moore complex ≤ 1 give the crossed modulus structure.
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Conclusion & Impact:If we take NE_00={0}, we have proved that the new structure obtained forms a crossed corner structure.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Çaprazlanmış modül · Çaprazlanmış köşe · bisimplisel cebir

Abstract

A simplicial algebra models algebraic structures that correspond to homotopy types. In this regard, simplicial algebras with a dimension of Moore complex ≤ 1 give the crossed modulus structure. When the length of the Moore complex is ≤ 2, 2-crossed modules, crossed squares, or structures equivalent to cat2 algebras are obtained. When the first component of simplicial algebra is taken as a unit, a reduced simplicial algebra structure is formed, and this structure models 1-connected homotopy types. In this study, we will show how bisimplicial algebras model the concept of crossed corners. In this structure, taking advantage of the equivalence of the category of crossed squares on commutative algebras and the category of simplicial commutative algebras of the Moore complex of length 2. If we take NE_00={0}, we have proved that the new structure obtained forms a crossed corner structure.

Özet

Bir simplisel cebir, homotopi tiplerine karşılık gelen cebirsel yapıları modeller. Bu bağlamda, Moore kompleksinin boyutu ≤ 1 olan simplisel cebirler, çaprazlanmış modül yapısını vermektedir. Moore kompleksinin boyutu ≤ 2 olduğunda 2-çaprazlanmış modüller, çaprazlanmış kareler veya cat2-cebirlere denk yapılar elde edilmektedir. Simplisel cebirin ilk bileşeni birim alındığında indirgenmiş simplisel cebir yapısı oluşur ve bu yapı 1- bağlantılı homotopi tiplerine modelleme yapar. Bu çalışmada bisimplisel cebirlerin, çaprazlanmış köşe kavramını nasıl modellediği göstererildi. Değişmeli cebirler üzerinde çaprazlanmış kare kategorisi ile Moore kompleksinin boyutu 2 olan simplisel değişmeli cebirler kategorisinin denkliğinden yararlanarak bu yapıda NE_00={0} alırsak elde ettiğimiz yeni yapının bir çaprazlanmış köşe yapısı oluşturduğunu ispatladık.

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Cite This Article

Binbir, H., Alansal, Ö. G. (2024). Crossed Corner of Commutative Algebra and Moore BiComplex. Kırşehir Ahi Evran Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 2 Sayı: 1, 12–18. https://ajindex.com/articles/1645944

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