Weak Idempotent Rings
| dc.contributor.advisor | Venkateswarlu, Kolluru (Professor) | |
| dc.contributor.author | Wasihun, Dereje | |
| dc.date.accessioned | 2021-01-22T08:32:19Z | |
| dc.date.accessioned | 2023-11-04T12:31:08Z | |
| dc.date.available | 2021-01-22T08:32:19Z | |
| dc.date.available | 2023-11-04T12:31:08Z | |
| dc.date.issued | 2020-11-11 | |
| dc.description.abstract | We introduce the notion of Weak idempotent ring (WIR, for short) which is a ring of characteristic 2 and a4 = a2 for each a in the ring. We obtain certain properties of this class. Further we provide examples of weak idempotent rings to have more deeper insight in studying the structure of weak idempotent rings. An equivalent de_nition for a commutative WIR with unity is given. Also we obtain certain characterization theorems in terms of completely prime ideals and left completely primary ideals. We introduce the concept of one sided completely primary ideal and prove that a one sided completely primary ideal is completely prime if the ideal contains all nilpotent elements of the ring. Also we prove that every local weak idempotent ring with unity is primary ring and the intersection of all primary ideals of a commutative weak idempotent ring with unity is the zero ideal. We construct a partial synthesis of weak idempotent rings and develop a subclass 2-Weak idempotent rings of the class of weak idempotent rings. We investigate the structure of a weak idempotent ring with unity of 4 and 8 elements. Further we prove that every proper ideal is nil whenever 0 and 1 are the only idempotent elements of the weak idempotent ring with unity. We characterize the semiprime and primary ideals of commutative weak idempotent rings with unity and prove that the class weak idempotent rings satis_es the K othe's conjecture. We study the structure of submaximal ideals in a commutative weak idempotent ring with unity and show that every submaximal ideal of a commutative weak idempotent ring with unity is either semiprime or primary. We prove that every submaximal ideal of the product ring of two commutative WIRs with unity is semiprime and the intersection of all submaximal ideals is the nilradical. We make a study on the fraction of rings for commutative weak idempotent rings with unity. Finally, We obtain certain properties concerning submaximal ideals under homomorphic images. | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/24790 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Weak | en_US |
| dc.subject | Idempotent | en_US |
| dc.subject | Rings | en_US |
| dc.title | Weak Idempotent Rings | en_US |
| dc.type | Thesis | en_US |