On Commutativity of Prime Near-Rings by Generalized Derivations
| dc.contributor.advisor | Abebaw, Tilahun (PhD) | |
| dc.contributor.author | Wubshet, Tadesse | |
| dc.date.accessioned | 2019-10-07T06:04:30Z | |
| dc.date.accessioned | 2023-11-04T12:30:57Z | |
| dc.date.available | 2019-10-07T06:04:30Z | |
| dc.date.available | 2023-11-04T12:30:57Z | |
| dc.date.issued | 2018-06-03 | |
| dc.description.abstract | Given a nonempty set N together with two binary operations, called addition "+" and multiplication ".", if (N; +) is a group, (N; :) is a semigroup and multiplication is left or right distributive over addition, the algebraic structure (N;+; :) is called a near-ring. If (N;+; :) is a near ring, a function D : N ! N is said to be a derivation on N if D(xy) = D(x)y+xD(y) for all x; y 2 N and an additive mapping F : N ! N satisfying F(xy) = F(x)y + xD(y) for all x; y 2 N, is called generalized derivation on N associated with the derivation D. The aim of this thesis is to study the commutativity of a near-ring using properties of generalized derivations on the given near ring. If F is a generalized derivation on a near- ring N associated with a derivation D and if either F[x; y] + [x; y] = 0 for all x; y 2 N; F[x; y][x; y] = 0 for all x; y 2 N, F(xoy)(xoy) = 0 for all x; y 2 N or F(xoy)+(xoy) = 0 for all x; y 2 N, then it is proved that N is commutative, where [x; y] = xy yx and xoy = xy+yx for all x; y 2 N: In this thesis, the commutativity of 3-torsion free prime near- ring N involving generalized derivation F associated with non-zero idempotent derivation D on N, satisfying F2[x; y] [x; y] = 0 for all x; y 2 N and F2(xoy) (xoy) = 0 for all x; y 2 N and commutativity of 5-torsion free prime near ring N involving generalized derivation F associated with non-zero idempotent derivation D on N, satisfying F2[x; y] + [x; y] = 0 for all x; y 2 N and F2(xoy) + (xoy) = 0 for all x; y 2 N are proved. These results can be used to further study the commutativity of prime near-rings using generalized derivations de_ned on a near-ring. | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/19315 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Commutativity | en_US |
| dc.subject | Prime Near-Rings | en_US |
| dc.subject | Generalized Derivations | en_US |
| dc.title | On Commutativity of Prime Near-Rings by Generalized Derivations | en_US |
| dc.type | Thesis | en_US |