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A Study on Special Kinds of Derivations in Ordered Hyperrings.
- Source :
-
Symmetry (20738994) . Oct2022, Vol. 14 Issue 10, pN.PAG-N.PAG. 12p. - Publication Year :
- 2022
-
Abstract
- In this study, we concentrate on an important class of ordered hyperstructures with symmetrical hyperoperations, which are called ordered Krasner hyperrings, and discuss strong derivations and homo-derivations. Additionally, we apply our results on nonzero proper hyperideals to the study of derivations of prime ordered hyperrings. This work is a pioneer in studies on structures such as hyperideals and homomorphisms of an ordered hyperring with the help of derivation notation. Finally, we prove some results on 2-torsion-free prime ordered hyperrings by using derivations. We show that if d is a derivation of 2-torsion-free prime hyperring R and the commutator set [ l , d (q) ] is equal to zero for all q in R, then l ∈ Z (R) . Moreover, we prove that if the commutator set (d (l) , q) is equal to zero for all l in R, then (d (R) , q) = 0 . [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMMUTATION (Electricity)
*HOMOMORPHISMS
*COMMUTATORS (Operator theory)
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 14
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 159942485
- Full Text :
- https://doi.org/10.3390/sym14102205