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Higher derivations and jordan higher derivations of Г-rings |
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| รหัสดีโอไอ | |
| Title | Higher derivations and jordan higher derivations of Г-rings |
| Creator | Julalak Kaewwangsakoon |
| Contributor | Sajee Pianskool |
| Publisher | Chulalongkorn University |
| Publication Year | 2553 |
| Keyword | Derivation, Jordan derivation, Higher derivations, Mathematical analysis, คณิตศาสตร์วิเคราะห์, อนุพันธ์ |
| Abstract | Let M and Г be additive abelian groups. If there exists a map ⋅ sending M x Г x M into M, denote the image of a ⋅ γ ⋅ b by, simply, aγb for all a, b ϵ M and γ ϵ Г, satisfying the following properties: for each a, b, c ϵ M and γ, β ϵ Г, (i) (aγb)βc = aγ(bβc); (ii) (a + b)γc = aγc + bγc, a(γ + β)c = aγc + aβc and aγ(b + c) = aγb + aγc, then M is called a Г-ring. Let M be a Г-ring and U be an ideal of M. We introduce the concept of higher derivations, Jordan higher derivations of M, higher derivations, Jordan higher derivations of U into M and generalized higher derivations, Jordan generalized higher derivations of M. Our main interests are finding appropriate conditions for a Г-ring in order to obtain that 1. Jordan higher derivations and higher derivations of a Г-ring are the same, 2. Jordan higher derivations and higher derivations of an ideal of a Г-ring, are identical, and 3. Jordan generalized higher derivations and generalized higher derivations of a Г-ring are coincide. |
| URL Website | cuir.car.chula.ac.th |
