Project on a Generalization of Boolean Rings
| dc.contributor.advisor | enkateswarlu, K.V(PhD) | |
| dc.contributor.author | Assefa, Abebaye | |
| dc.date.accessioned | 2018-07-11T06:52:46Z | |
| dc.date.accessioned | 2023-11-04T12:31:08Z | |
| dc.date.available | 2018-07-11T06:52:46Z | |
| dc.date.available | 2023-11-04T12:31:08Z | |
| dc.date.issued | 2011-06 | |
| dc.description.abstract | In this paper we introduce the concept of Boolean ring and 𝑅𝑅 satisfy the identity 𝑥𝑥2=𝑥𝑥 which, of course, implies the identity 𝑥𝑥2𝑦𝑦−𝑥𝑥𝑦𝑦2=0. With this as motivation, we define a Boolean like ring and subBoolean ring 𝑅𝑅 to be a ring 𝑅𝑅 which satisfies the condition that 𝑥𝑥2𝑦𝑦−𝑥𝑥𝑦𝑦2 is nilpotent for certain elements 𝑥𝑥,𝑦𝑦 in 𝑅𝑅. A strongly Boolean ring is a ring which 𝑥𝑥2𝑦𝑦=𝑥𝑥𝑦𝑦2 for some elements 𝑥𝑥,𝑦𝑦 in 𝑅𝑅. The commutativity behavior of such rings is considered. Also, certain conditions which imply that these rings have a nil commutator ideal are established. We consider some conditions which imply that the subBoolean ring 𝑅𝑅 is commutative or has a nil commutator ideal. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which imply the commutativity of a generalized Boolean ring | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/7816 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Project on a Generalization | en_US |
| dc.title | Project on a Generalization of Boolean Rings | en_US |
| dc.type | Thesis | en_US |