Abstract
In this paper, we introduce and study the notions of n-strongly Gorenstein projective and injective complexes, which are generalizations of n-strongly Gorenstein projective and injective modules, respectively. Further, we characterize the so-called notions and prove that the Gorenstein projective (resp., injective) complexes are direct summands of n-strongly Gorenstein projective (resp., injective) complexes. Also, we discuss the relationships between n-strongly Gorenstein injective and n-strongly Gorenstein flat complexes, and for any two positive integers n and m, we exhibit the relationships between n-strongly Gorenstein projective (resp., injective) and m-strongly Gorenstein projective (resp., injective) complexes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anderson, F.W., Fuller, K.R.: Rings and Categories of Modules. Graduate Texts in Mathematics, vol. 13, 2nd edn. Springer, New York (1992)
Bennis, D., Mahdou, N.: Strongly Gorenstein projective, injective and flat modules. J. Pure Appl. Algebra 210, 437–445 (2007)
Bennis, D., Mahdou, N.: A generalization of strongly Gorenstein projective modules. J. Algebra Appl. 8, 219–227 (2009)
Enochs, E., GarcÃa Rozas, J.R.: Tensor products of complexes. Math. J. Okayama Univ. 39, 17–39 (1997)
Enochs, E., Jenda, O.M.G.: Relative Homological Algebra. de Gruyter Expositions in Mathematics, vol. 30. Walter de Gruyter, Berlin (2000)
GarcÃa Rozas, J.R.: Covers and Envelopes in the Category of Complexes of Modules. CRC Press, Boca Raton (1999)
Selvaraj, C., Saravanan, R.: \(SG\)-flat complexes and their generalizations, communicated to Vietnam J. Math
Yang, X., Liu, Z.: Strongly Gorenstein projective, injective and flat modules. J. Algebra 320, 2659–2674 (2008)
Yang, X., Liu, Z.: Gorenstein projective, injective and flat complexes. J. Commut. Algebra 39, 1705–1721 (2011)
Zhang, D., Ouyang, B.: Strongly Gorenstein projective and injective complexes. J. Nat. Sci. Hunan Norm. Univ. 35, 1–5 (2012)
Zhao, G., Huang, Z.: \(n\)-strongly Gorenstein projective, injective and flat modules. Commun. Algebra 39, 3044–3062 (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media Singapore
About this paper
Cite this paper
Selvaraj, C., Saravanan, R. (2016). n-Strongly Gorenstein Projective and Injective Complexes. In: Rizvi, S., Ali, A., Filippis, V. (eds) Algebra and its Applications. Springer Proceedings in Mathematics & Statistics, vol 174. Springer, Singapore. https://doi.org/10.1007/978-981-10-1651-6_17
Download citation
DOI: https://doi.org/10.1007/978-981-10-1651-6_17
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-1650-9
Online ISBN: 978-981-10-1651-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)