t-extending Krasner hypermodules
Resumo
Let M be a hypermodule over a hyperring R such that the intersection of any two subhypermodules of M is a subhypermodule of M. We introduce the concept of an t-essential subhypermodule in M relative to an arbitrary subhypermodule T of M, which is called T-t-essential subhypermodule of M. Our aim in this work is to investigate properties of t-essential subhypermodules. We apply this concept to introduce t-extending hypermodules. Examples are provided to illustrate different concepts.
Downloads
Referências
Ameri, R., On categories of hypergroups and hypermodules, Journal of Discrete Mathematical Sciences 6(2-3), 121-132, (2003). https://doi.org/10.1080/09720529.2003.10697969
Anderson, F. W., Fuller, K. R., Rings and Categories of Modules, Springer-Verlag, New York (1992). https://doi.org/10.1007/978-1-4612-4418-9
Anvariyeh, S. M., Davvaz, B., Strongly transitive geometric spaces associated to hypermodules, Journal of Algebra 322, 1340-1359, (2009). https://doi.org/10.1016/j.jalgebra.2009.05.014
Asgari, S. H., Haghany, A., t-extending Modules and t-Baer Modules, Communications in Algebra 39, 1605-1623, (2011). https://doi.org/10.1080/00927871003677519
Corsini, P., Prolegomena of Hypergroup Theory, 2nd ed. Tricesimo Italy, Aviani editore Italy, (1993).
Davvaz, B., Remarks on weak hypermodules, Bull. Korean Math. Soc. 36(3), 599-608, (1999).
Davvaz, B., Fotea, V. L., Hyperring Theory and Applications, Palm Harbor, FL, USA International Academic Press, (2007).
Fotea, V. L., uzzy hypermodules, Computers and Mathematics with Applications 57, 466-475, (2009). https://doi.org/10.1016/j.camwa.2008.11.004
Hamzekolaee, A. R. M., Norouzi, M., A hyperstructural approach to essentially, Communications In Algebra 46(11), 4954-4964, (2018). https://doi.org/10.1080/00927872.2018.1459649
Krasner, M., A class of hyperrings and hyperfields, IJMMS 6(2), 307-311, (1999). https://doi.org/10.1155/S0161171283000265
Omidi, S., Davvaz, B., Hyperideal theory in ordered Krasner hyperrings, An. S¸t. Univ. Ovidius Constanta 27(1), 193-210, (2019). https://doi.org/10.2478/auom-2019-0010
Lam, T. Y., Lectures on Modules and Rings, Graduate Texts in Mathematics. 189, New York, Springer-Verlag, (1998). https://doi.org/10.1007/978-1-4612-0525-8
Wisbauer, R., Foundations of module and ring theory, Gordon and Breach, (1991).
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
