Various Kinds of Freeness in the Categories of Krasner Hypermodules

Article Sidebar

PDF
Cite as:
Hossein Shojaei, Reza Ameri, Various Kinds of Freeness in the Categories of Krasner Hypermodules, Int. J. Anal. Appl., 16 (6) (2018), 793-808.

Main Article Content

Hossein Shojaei, Reza Ameri

Abstract

The purpose of this paper is to study the concept of freeness in the categories of Krasner hypermodules over a Krasner hyperring. In this regards first we construct various kinds of categories of hypermodules based on various kinds of homomorphisms of hypermodules, such as homomorphisms, good homomorphisms, multivalued homomorphisms and etc. Then we investigate the notion of free hypermodule in these categories. This leads us to introduce different types of free, week free, *-free and fundamental free hypermodules and obtain the relationship among them.

Article Details

References

  1. R. Ameri, On categories of hypergroups and hypermodules, J. Discrete Math. Sci. Cryptogr. 6(2-3) (2003), 121-132.
  2. S. Awodey, Category theory, Second ed., Oxford University Press, Inc. New York, 2010.
  3. P. Corsini, Prolegomena of Hypergroup Theory, Second ed., Aviani Editore, Tricesimo, 1993.
  4. P. Corsini and V. Leoreanu-Fotea, Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publication, Dordrecht, 2003.
  5. B. Davvaz, A brief survey of the theory of Hv-structures, 8th AHA, Greece, Spanidis (2003), 39-70.
  6. B. Davvaz, Polygroup Theory and Related Systems, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013.
  7. B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, Palm Harbor, USA, 2007.
  8. H. Herrlich and G. E. Strecker, Category theory, Vol. 2. Boston: Allyn and Bacon, 1973.
  9. M. Krasner, A class of hyperrings and hyperfelds, Internat. J. Math. Math. Sci. 6 (1983), 307-311.
  10. Ch G. Massouros, Free and cyclic hypermodules, Ann. Math. Pura Appl. 150 (1) (1988), 153-166.
  11. F. Marty, Sur uni generalization de la notion de group, in: 8th Congress Math. Scandenaves, Stockholm, (1934), 45-49.
  12. S. Sh. Mousavi and M. Jafarpour, On Free and Weak Free (Semi) Hypergroups, Algebra Colloq. 18 (2011), 873-880.
  13. A. Nakassis, Expository and survey article of recent results in hyperring and hyperfield theory, Internat. J. Math. Math. Sci. 11 (1988) 209-220.
  14. H. Shojaei and R. Ameri, Some results on categories of Krasner hypermodules, J. Fundam. Appl. Sci. 8 (3S) (2016), 2298-2306.
  15. H. Shojaei, R. Ameri and S. Hoskova-Mayerova, On properties of various morphisms in the categories of general Krasner hypermodules, Italian J. Pure Appl. Math. 39 (2018), 475-484.
  16. T. Vougiouklis, The fundamental relation in hyperrings, The general hyperfeld, 4th AHA, Xanthi 1990, World Scientifc (1991), 203-211.
  17. T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Inc., 115, Palm Harber, USA, 1994.