Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 6

Higher dimensional algebras as ideal maps

Sayfa
1865–1884
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also explain this structure for crossed squares of algebras.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, we explain the close relationship between an ideal map structure $S\rightarrow End_{R}(R)$ on a homomorphism of commutative $k$-algebras $R\rightarrow S$ and an ideal simplicial algebra structure on the associated bar construction $Bar(S,R)$.
📊
Temel Bulgular & Veri:In this work, we explain the close relationship between an ideal map structure $S\rightarrow End_{R}(R)$ on a homomorphism of commutative $k$-algebras $R\rightarrow S$ and an ideal simplicial algebra structure on the associated bar construction $Bar(S,R)$.
💡
Sonuç & Katkı:We also explain this structure for crossed squares of algebras.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:crossed module · crossed square · ideal map

Abstract

In this work, we explain the close relationship between an ideal map structure $S\rightarrow End_{R}(R)$ on a homomorphism of commutative $k$-algebras $R\rightarrow S$ and an ideal simplicial algebra structure on the associated bar construction $Bar(S,R)$. We also explain this structure for crossed squares of algebras.

🔖

Bu Makaleye Atıf Yap

Odabaş, A., Ulualan, E. (2022). Higher dimensional algebras as ideal maps. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 6, 1865–1884. https://ajindex.com/articles/530053

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (16)

  1. M. André, Homologie des algèbres commutatives, Die Grundlehren der Mathematischen Wissenchaften, 206 Springer-Verlag 1974
  2. Z. Arvasi and T. Porter, Higher dimensional Peiffer elements in simplicial commutative algebras, Theory Appl. Categ., 3, No. 1, pp 1-23, 1997
  3. Z. Arvasi and T. Porter, Freeness conditions for 2-crossed module of commutative algebras, Appl. Categ. Structures, 6, 455-471, 1998
  4. Z. Arvasi and A. Odabaş, Computing 2-dimensional algebras: Crossed modules and Cat1-algebras, J. Algebra Appl. 15 (10), 1650185, 2016
  5. T. Datuashvili and T. Pirashvili, On Co Homology of 2-Types and Crossed Modules, J. Algebra 244, 352-365, 2001
  6. G. Ellis, Higher dimensional crossed modules of algebras, J. Pure Appl. Algebra 52, 277-282, 1988
  7. G. Ellis, Crossed squares and combinatorial homotopy, Math. Z. 214, 93-110, 1993
  8. E.D. Farjoun and K. Hess, Normal and co-normal maps in homotopy theory, Homology Homotopy Appl. 14, 1, 79-112, 2012
  9. E.D. Farjoun and Y. Segev, Crossed modules as homotopy normal maps, Topology Appl. 157, 359-368, 2010
  10. E.D. Farjoun and Y. Segev, Normal closure and injective normalizer of a group homomorphism, J. Algebra 423, 1010-1043, 2015
  11. D. Guin-Waléry and J-L. Loday, Obsructioná l’excision en K-theories algébrique, In: Friedlander, E.M.,Stein, M.R.(eds.) Evanston conf. on algebraic K-Theory 1980, (Lecture Notes in Math., 854, 179-216), Springer, Berlin Heidelberg, 1981
  12. L. Illusie, Complex cotangent et deformations I, II, Lecture Notes in Math. 239 1971, II: 283, Springer, 1972
  13. T. Porter, Homology of commutative algebras and an invariant of Simis and Vasconceles, J. Algebra 99, 458-465, 1986
  14. M. Prezma, Homotopy normal maps, Algebr. Geom. Topol. 12, 1211-1238, 2012
  15. N.M. Shammu, Algebraic and categorical structure of category of crossed modules of algebras, University of Wales, PhD Thesis, 1992
  16. J.H.C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc. 55, 453-496, 1949.