Main Article Content
Abstract
axioms is the class of Hv-rings (Hv-fields). In this paper, we define the Hv-integral
domain and introduce the Hv-field of fractions of an Hv-integral domain. Also, the
Hv-quotient ring and some relative theorems are presented. Finally, some interesting
results about the Hv-rings of fractions, Hv-quotient rings and the relations between
them are proved.
Keywords
Article Details
References
- M. R. Darafsheh, B. Davvaz, Hv-ring of Fractions, Italian J. Pure Appl. Math. 5 (1999), 25-34.
- B. Davvaz, Remark on Weak Hypermodules, Bull. Korean Math. Soc. 36 (1999), no. 3, 599-608.
- B. Davvaz and M. Ghadiri, Weak equality and exact sequences in Hv-modules, Southeast Asian Bull. Math. 25 (2001), no. 3, 403-411.
- M. Ghadiri and B. Davvaz, Direct System and Direct Limit of Hv-modules, Iran. J. Sci. Technol. Trans. A Sci. 28 (2004), no. 2, 267-275.
- M. Ghadiri and B. N. Waphare, n-ary P-Hv-Groups, J. Appl. Math. & Informatics 26 (2008), no. 5-6, 445-959.
- M. Ghadiri, B. N. Waphare and B. Davvaz, Quotient n-ary P-Hv-ring, Carpathian J. Math.28 (2012), no. 2, 239-246.
- F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm. (1934), 45-49.
- S. Spartalis, On the number of Hv-rings with P-hyperoperations, Discrete Math. 155 (1996), no. 1-3, 225-231.
- S. Spartalis and T. Vougiouklis, The Fundamental Relations in Hv-rings, Rivista Math. Pura ppl. 14 (1994) 7-20.
- T. Vougiouklis , The Fundamental Relations in Hyperrings. The General Hyperfield, Proc. Fourth Int. Congress on Algebraic Hyperstructures and Applications (AHA 1990), Scientific (1991) 203-211.
- T. Vougiouklis, Convolutions on WASS hyperstructures, Discrete Math. 174 (1997), 347-355.
- T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press Inc., Florida, 1994.
- T. Vougiouklis, On Hv-rings and Hv-representations, Discrete Math. 208-209 (1999) 615-620.
References
M. R. Darafsheh, B. Davvaz, Hv-ring of Fractions, Italian J. Pure Appl. Math. 5 (1999), 25-34.
B. Davvaz, Remark on Weak Hypermodules, Bull. Korean Math. Soc. 36 (1999), no. 3, 599-608.
B. Davvaz and M. Ghadiri, Weak equality and exact sequences in Hv-modules, Southeast Asian Bull. Math. 25 (2001), no. 3, 403-411.
M. Ghadiri and B. Davvaz, Direct System and Direct Limit of Hv-modules, Iran. J. Sci. Technol. Trans. A Sci. 28 (2004), no. 2, 267-275.
M. Ghadiri and B. N. Waphare, n-ary P-Hv-Groups, J. Appl. Math. & Informatics 26 (2008), no. 5-6, 445-959.
M. Ghadiri, B. N. Waphare and B. Davvaz, Quotient n-ary P-Hv-ring, Carpathian J. Math.28 (2012), no. 2, 239-246.
F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm. (1934), 45-49.
S. Spartalis, On the number of Hv-rings with P-hyperoperations, Discrete Math. 155 (1996), no. 1-3, 225-231.
S. Spartalis and T. Vougiouklis, The Fundamental Relations in Hv-rings, Rivista Math. Pura ppl. 14 (1994) 7-20.
T. Vougiouklis , The Fundamental Relations in Hyperrings. The General Hyperfield, Proc. Fourth Int. Congress on Algebraic Hyperstructures and Applications (AHA 1990), Scientific (1991) 203-211.
T. Vougiouklis, Convolutions on WASS hyperstructures, Discrete Math. 174 (1997), 347-355.
T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press Inc., Florida, 1994.
T. Vougiouklis, On Hv-rings and Hv-representations, Discrete Math. 208-209 (1999) 615-620.