Pro-C completions of crossed squares of commutative algebras

Year 2020, Volume: 69 Issue: 1, 320 - 335, 30.06.2020

Hatice Gülsün Akay

https://doi.org/10.31801/cfsuasmas.556898

Abstract

In this paper we give the explicit construction of a pro-C completion functor which is defined in the category of crossed squares of commutative algebras. Afterwards, we study some functorial properties of this pro-C completion process.

Keywords

Crossed square, pro-C crossed square, pro-C completion

References

• Arvasi, Z., Crossed squares and 2-crossed modules of commutative algebras, Theory and Applications of Categories, 3(7), (1997), 160--181.
• Arvasi, Z. and Ege, U., Annihilators, multipliers and crossed modules, Applied Categorical Structures, 11, (2003), 487--506.
• Aytekin, A. and Koçak, M., Pro-C completions process of crossed squares and some relations, World Applied Sciences Journal, 7 (7), (2009), 856--865.
• Ellis, G.J., Higher dimensional crossed modules of algebras, J. Pure and Appl. Algebra, 52, (1988), 277--282.
• Ellis, G.J., Crossed modules and their higher dimensional analogues, University of Wales, Ph.D. Thesis, (1984).
• Koçak, M., Pro-C completions of crossed modules of commutative algebras, Algebras, Groups and Geometries, Vol 22(2), (2005).
• Kokers, K.J. and Porter, T., Pro-C completions of crossed modules, Proceedings of the Edinburgh Mathematical Society, 33-1 (1990), 39--51.
• Porter, T., Homology of commutative algebras and an invariant of Simis and Vasconceles, J.Algebra, 99, 2, (1987).
• Ribes, L. and Zalesskii, P., Profinite groups, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, Springer-Verlag, Berlin, (2000).
• Whitehead, J.H.C., Combinatorial homotopy II., Bull. Amer. Math. Soc., 55, (1949), 213--245.