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Year 2020, , 32 - 41, 15.10.2020
https://doi.org/10.36753/mathenot.718833

Abstract

References

  • [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

Year 2020, , 32 - 41, 15.10.2020
https://doi.org/10.36753/mathenot.718833

Abstract

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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References

  • [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).
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Elis Soylu Yılmaz 0000-0002-0869-310X

Koray Yılmaz 0000-0002-8641-0603

Publication Date October 15, 2020
Submission Date April 12, 2020
Acceptance Date August 1, 2020
Published in Issue Year 2020

Cite

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. October 2020;8(2):32-41. doi:10.36753/mathenot.718833
Chicago Soylu Yılmaz, Elis, and Koray Yılmaz. “On Crossed Squares of Commutative Algebras”. Mathematical Sciences and Applications E-Notes 8, no. 2 (October 2020): 32-41. https://doi.org/10.36753/mathenot.718833.
EndNote Soylu Yılmaz E, Yılmaz K (October 1, 2020) On Crossed Squares of Commutative Algebras. Mathematical Sciences and Applications E-Notes 8 2 32–41.
IEEE E. Soylu Yılmaz and K. Yılmaz, “On Crossed Squares of Commutative Algebras”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 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 (October 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 and Koray Yılmaz. “On Crossed Squares of Commutative Algebras”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, 2020, pp. 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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