A new approach to smallness in hypermodules

Document Type : Research Paper


1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

2 Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran

3 Faculty of Mathematics, University of Al.I. Cuza of Iasi, Iasi, Romania



In this paper, we extend the concept of small subhypermodules to all types of hypermodules and give nontrivial examples for this concept. As an application, we define and study lifting hypermodules via small subhypermodules.


[1] S. M. Anvariyeh and B. Davvaz, Strongly transitive geometric spaces associated to hypermodules, J. Algebra, Vol. 322 (2009), pp. 1340–1359.
[2] S. M. Anvariyeh and B. Davvaz, On the heart of hypermodules, Math. Scand. Vol. 106 (2010), pp. 39–49.
[3] S. M. Anvariyeh and S. Mirvakili, Canonical (m, n)-ary hypermodules over Krasner (m, n)-ary hyperrings, Iran. J. Math. Sci. Inform. Vol. 7 No. 2 (2012), pp. 17–34.
[4] J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting Modules: Supplements and Projectivity in Module Theory Frontiers in Mathematics, Boston, Birkhuser, (2006).
[5] P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, (1993).
[6] P. Corsini, V. Leoreanu-Fotea, Applications of Hyperstructure Theory, Kluwer Academic Publishers, (2003).
[7] B. Davvaz, Polygroup Theory and Related Systems, World Scientific Publishing Co. (2013).
[8] B. Davvaz, V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, (2007).
[9] D. Keskin, On lifting modules, Comm. Algebra Vol. 28 No. 7 (2000), pp. 3427–3440.
[10] W. W. Leonard, Small modules, Proc. Amer. Math. Soc. Vol. 17 (1966), pp. 527–531.
[11] F. Marty, Sur une generalization de la notion de groupe, 8iem congres des Mathematiciens Scandinaves, Stockholm (1934), pp. 45–49.
[12] S. H. Mohamed and B. J. M¨uller, Continuous and Discrete Modules, London Math. Soc. Lecture Notes Series 147, Cambridge, University Press, (1990).
[13] A. R. Moniri Hamzekolaee and M. Norouzi, A hyperstructural approach to essentiality, Comm. Algebra Vol. 46 No. 11 (2018), pp. 4954–4964.
[14] B. Talaee, Small subhypermodules and their applications, Roman. J. Math. Comput. Soc. Vol. 3 No. 1 (2013), pp. 5–14.
[15] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading, (1991).
[16] T. Vougiouklis, Hyperstructures and Their Representations Hadronic, press, Inc. (1994).