Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 8 Sayı: 2, 32 - 41, 15.10.2020
https://doi.org/10.36753/mathenot.718833

Öz

Kaynakça

  • [1] Whitehead, J.H.C.: Combinatorial homotopy II. Bull. Amer. Math. Soc. 55, 453-496 (1949) .
  • [2] Ellis G.: Higher-dimensional crossed module of algebras. Journal of Pure and Applied Algebra. 52, 277-282 (1988).
  • [3] Arvasi Z.: Crossed Squares and 2 Crossed Modules of Commutative Algebras. Theory and Applications of Categories. 3 (7), 160-181 (1997).
  • [4] Arvasi Z., Porter, T.: Higher-dimensional Peiffer elements in simplicial Commutative Algebras. Theory and Applications of Categories. 3 (1), 1-23 (1997).
  • [5] Arvasi Z., Porter T.: Simplicial and Crossed Resolutions of Commutative Algebras. Journal of Algebra. 181, 426-448 (1996).
  • [6] Brown, R., Higgins, P.: On the Connection between the Second Relative Homotopy Groups of some Related Spaces. Proc. London Math. Soc. 36(2), 193-212 (1978).
  • [7] Brown, R., Sivera. R.: Algebraic colimit calculations in homotopy theory using fibred and cofibred categories. Theory and Application of Categories. 22(8), 222-251 (2009).
  • [8] Porter, T.: Homology of commutative algebras and an invariant of Simis and Vasconcelos. Journal of Algebra. 99, 458-465 (1986).
  • [9] Gerstenhaber, M.: On the deformation of rings and algebras. Annual of Mathematics. 84, 1-19 (1966).
  • [10] Lichtenbaum, S., Schlessinger, M.: The cotangent complex of a morphism. Transection American Mathematics Society. 128, 41-70 (1967).
  • [11] Guin-Waléry, D., Loday, J-L.: Obstructioná l’excision en K-théorie algébrique, in: Algebraic K-Theory (Evanston 1980). Lecture Notes in Math. 854, 179-216 (1981).
  • [12] Conduché, D.: Modules croisés généralisés de longueur 2. Journal of Pure and Applied Algebra. 34, 155-178 (1984).
  • [13] Arvasi, Z., Ulualan, E.: Quadratic and 2-crossed modules of algebras. Algebra Colloquium. 14, 669-686 (2007).
  • [14] Grandjéan, A.R., Vale, M,J.: 2-Modulos cruzados an la cohomologia de André- Quillen. Memorias de la Real Academia de Ciencias. 22, 1-28 (1986).
  • [15] Shammu, N.M.: Algebraic and categorical structure of categories of crossed modules of algebras. Ph.D. thesis. University College of NorthWales (1992).

On Crossed Squares of Commutative Algebras

Yıl 2020, Cilt: 8 Sayı: 2, 32 - 41, 15.10.2020
https://doi.org/10.36753/mathenot.718833

Öz

In this work, we show a categorical property for crossed squares of commutative algebras by defining a specific object in this category and then we give the construction of the pullback with this object. ................................................................................................ .....................................................................................................

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Kaynakça

  • [1] Whitehead, J.H.C.: Combinatorial homotopy II. Bull. Amer. Math. Soc. 55, 453-496 (1949) .
  • [2] Ellis G.: Higher-dimensional crossed module of algebras. Journal of Pure and Applied Algebra. 52, 277-282 (1988).
  • [3] Arvasi Z.: Crossed Squares and 2 Crossed Modules of Commutative Algebras. Theory and Applications of Categories. 3 (7), 160-181 (1997).
  • [4] Arvasi Z., Porter, T.: Higher-dimensional Peiffer elements in simplicial Commutative Algebras. Theory and Applications of Categories. 3 (1), 1-23 (1997).
  • [5] Arvasi Z., Porter T.: Simplicial and Crossed Resolutions of Commutative Algebras. Journal of Algebra. 181, 426-448 (1996).
  • [6] Brown, R., Higgins, P.: On the Connection between the Second Relative Homotopy Groups of some Related Spaces. Proc. London Math. Soc. 36(2), 193-212 (1978).
  • [7] Brown, R., Sivera. R.: Algebraic colimit calculations in homotopy theory using fibred and cofibred categories. Theory and Application of Categories. 22(8), 222-251 (2009).
  • [8] Porter, T.: Homology of commutative algebras and an invariant of Simis and Vasconcelos. Journal of Algebra. 99, 458-465 (1986).
  • [9] Gerstenhaber, M.: On the deformation of rings and algebras. Annual of Mathematics. 84, 1-19 (1966).
  • [10] Lichtenbaum, S., Schlessinger, M.: The cotangent complex of a morphism. Transection American Mathematics Society. 128, 41-70 (1967).
  • [11] Guin-Waléry, D., Loday, J-L.: Obstructioná l’excision en K-théorie algébrique, in: Algebraic K-Theory (Evanston 1980). Lecture Notes in Math. 854, 179-216 (1981).
  • [12] Conduché, D.: Modules croisés généralisés de longueur 2. Journal of Pure and Applied Algebra. 34, 155-178 (1984).
  • [13] Arvasi, Z., Ulualan, E.: Quadratic and 2-crossed modules of algebras. Algebra Colloquium. 14, 669-686 (2007).
  • [14] Grandjéan, A.R., Vale, M,J.: 2-Modulos cruzados an la cohomologia de André- Quillen. Memorias de la Real Academia de Ciencias. 22, 1-28 (1986).
  • [15] Shammu, N.M.: Algebraic and categorical structure of categories of crossed modules of algebras. Ph.D. thesis. University College of NorthWales (1992).
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Elis Soylu Yılmaz 0000-0002-0869-310X

Koray Yılmaz 0000-0002-8641-0603

Yayımlanma Tarihi 15 Ekim 2020
Gönderilme Tarihi 12 Nisan 2020
Kabul Tarihi 1 Ağustos 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 2

Kaynak Göster

APA Soylu Yılmaz, E., & Yılmaz, K. (2020). On Crossed Squares of Commutative Algebras. Mathematical Sciences and Applications E-Notes, 8(2), 32-41. https://doi.org/10.36753/mathenot.718833
AMA Soylu Yılmaz E, Yılmaz K. On Crossed Squares of Commutative Algebras. Math. Sci. Appl. E-Notes. Ekim 2020;8(2):32-41. doi:10.36753/mathenot.718833
Chicago Soylu Yılmaz, Elis, ve Koray Yılmaz. “On Crossed Squares of Commutative Algebras”. Mathematical Sciences and Applications E-Notes 8, sy. 2 (Ekim 2020): 32-41. https://doi.org/10.36753/mathenot.718833.
EndNote Soylu Yılmaz E, Yılmaz K (01 Ekim 2020) On Crossed Squares of Commutative Algebras. Mathematical Sciences and Applications E-Notes 8 2 32–41.
IEEE E. Soylu Yılmaz ve K. Yılmaz, “On Crossed Squares of Commutative Algebras”, Math. Sci. Appl. E-Notes, c. 8, sy. 2, ss. 32–41, 2020, doi: 10.36753/mathenot.718833.
ISNAD Soylu Yılmaz, Elis - Yılmaz, Koray. “On Crossed Squares of Commutative Algebras”. Mathematical Sciences and Applications E-Notes 8/2 (Ekim 2020), 32-41. https://doi.org/10.36753/mathenot.718833.
JAMA Soylu Yılmaz E, Yılmaz K. On Crossed Squares of Commutative Algebras. Math. Sci. Appl. E-Notes. 2020;8:32–41.
MLA Soylu Yılmaz, Elis ve Koray Yılmaz. “On Crossed Squares of Commutative Algebras”. Mathematical Sciences and Applications E-Notes, c. 8, sy. 2, 2020, ss. 32-41, doi:10.36753/mathenot.718833.
Vancouver Soylu Yılmaz E, Yılmaz K. On Crossed Squares of Commutative Algebras. Math. Sci. Appl. E-Notes. 2020;8(2):32-41.

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