Abstract
In this paper we introduce the concept of \(\xi \)-torsion module, \(\xi \)-torsion-free module and \(\xi \)-torsionable module. We investigate many properties of these modules. We characterize \(\xi \)-torsion modules and \(\xi \)-torsion-free modules using short exact sequences and module homomorphisms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aluffi, P.: Algebra. American Mathematical Society, USA (2009)
Azizi, A.: Prime submodules of Artinian modules. Taiwan. J. Math. 13, 2011–2020 (2009)
Barnard, A.: Multiplication modules. J. Algebra 71, 174–178 (1981)
Goodearl, K.R.: Ring Theory: Nonsingular Rings and Modules. Marcel Dekkar INC, New York (1976)
Lam, T.Y.: Lectures on Modules and Rings. Springer, New York (1999)
Lambek, J.: Lectures on Ring and Modules. Mc Gill University, Montreal (1962)
Rotman, J.J.: Homological Algebra, 2nd edn. Springer, New York (2009)
Acknowledgments
Author’s are grateful to Prof. K. R. Goodearl, Department of Mathematics, University of California, for fruitful discussions and valuable suggestions to improve this paper. All the Author’s acknowledge UGC for financial support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kalita, H., Hoque, A. & Saikia, H.K. On \(\xi \)-torsion modules. Boll Unione Mat Ital 10, 223–228 (2017). https://doi.org/10.1007/s40574-016-0076-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40574-016-0076-y