p-clean properties in amalgamated rings
Let A be a ring. Then A is called p-clean ring if each element in A express as the sum of an idempotent and pure element. Let f : A → B be a ring homomorphism and J be an ideal of B. The amalgamation of A with B along J with respct to f is a new ring structure introduced and studied by Anna et al. i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Accademia Piceno Aprutina dei Velati
2023-06-01
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| Series: | Ratio Mathematica |
| Subjects: | |
| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/958 |
| Summary: | Let A be a ring. Then A is called p-clean ring if each element in A express as the sum of an idempotent and pure element. Let f : A → B be a ring homomorphism and J be an ideal of B. The amalgamation of A with B along J with respct to f is a new ring structure introduced and studied by Anna et al. in 2009. This construction is a generalization of the amalgamated duplication of a ring along an ideal and other classical constructions such as the A + XB[X] and A + XB[[X]] constuctions. In this paper, the transfer of the notion of p-clean rings to the amalgamation of rings along ideal is studied. In particular, the necessary and sufficient conditions for amalgamation to be a p-clean ring are studied. |
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| ISSN: | 1592-7415 2282-8214 |