The New Results in n-injective Modules and n-projective Modules

  • Samira Hashemi Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
  • Feysal Hassani Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
  • Rasul Rasuli Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
Keywords: injective module, homomorphisms, n-ker and n-coker, n-injective module, n-projective module

Abstract

In this paper, we introduce and clarify a new presentation between the n-exact sequence and the n-injective module and n-projective module. Also, we obtain some new results about them.

References

M. Auslander and S. O. Smal$phi$, Almost split sequences in subcategories, J. Algebra 69(2) (1981), 426-454.

M. P. Brodmann and R. Y. Sharp, Local cohomology: an algebraic introduction with geometric applications, Cambridge Studies in Advanced Mathematics, vol. 60, Cambridge University Press, Cambridge, 1998.

T. Bühler, Exact categories, Expo. Math. 28(1) (2010), 1-69.

P. Freyd, Abelian categories: An introduction to the theory of functors, Harper's Series in Modern Mathematics, Harper and Row, New York, 1994.

L. Frerick and D. Sieg, Exact categories in functional analysis, Preprint 2010.

G. Jasso, n-abelian and n-exact categories, Math. Z. 283 (2016), 703–759.

A. Neeman, The derived category of an exact category, J. Algebra 135(2) (1990), 388-394.

L. Ribes and P. Zalesskii, Profinite Groups, Springer, 2010.

J. Rotman, An Introduction to Homological Algebra, Springer Verlag, New York, 2009.

C. A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, Cambridge, 2011.

Q. Zheng and J. Wei, Quotient categories of n-abelian categories, Glasgow Mathematical Journal 62(3) (2020), 673-705. https://doi.org/10.1017/S0017089519000417

P. Zhou and B. Zhu, n-abelian quotient categories, Journal of Algebra 527 (2019), 264-279. https://doi.org/10.1016/j.jalgebra.2019.03.007

Published
2021-08-19
How to Cite
Hashemi, S., Hassani, F., & Rasuli, R. (2021). The New Results in n-injective Modules and n-projective Modules. Earthline Journal of Mathematical Sciences, 7(2), 271-285. https://doi.org/10.34198/ejms.7221.271285
Section
Articles