On Crossed Squares of Commutative Algebras

Elis Soylu Yılmaz; Koray Yılmaz

doi:10.36753/mathenot.718833

EN

On Crossed Squares of Commutative Algebras

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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Keywords

Crossed module, Crossed square, Pullback

References

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[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).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Elis Soylu Yılmaz ^*
0000-0002-0869-310X
Türkiye

Koray Yılmaz
0000-0002-8641-0603
Türkiye

Publication Date

October 15, 2020

Submission Date

April 12, 2020

Acceptance Date

August 1, 2020

Published in Issue

Year 2020 Volume: 8 Number: 2

DOI

https://doi.org/10.36753/mathenot.718833

IZ

https://izlik.org/JA52YD76TH

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

1.Soylu Yılmaz E, Yılmaz K. On Crossed Squares of Commutative Algebras. Math. Sci. Appl. E-Notes. 2020;8(2):32-41. doi:10.36753/mathenot.718833

Chicago

Soylu Yılmaz, Elis, and Koray Yılmaz. 2020. “On Crossed Squares of Commutative Algebras”. Mathematical Sciences and Applications E-Notes 8 (2): 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

[1]E. Soylu Yılmaz and K. Yılmaz, “On Crossed Squares of Commutative Algebras”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 32–41, Oct. 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 1, 2020): 32-41. https://doi.org/10.36753/mathenot.718833.

JAMA

1.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, Oct. 2020, pp. 32-41, doi:10.36753/mathenot.718833.

Vancouver

1.Elis Soylu Yılmaz, Koray Yılmaz. On Crossed Squares of Commutative Algebras. Math. Sci. Appl. E-Notes. 2020 Oct. 1;8(2):32-41. doi:10.36753/mathenot.718833