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On rings with quasi-injective cyclic modules
| Content Provider | Scilit |
|---|---|
| Author | Ahsan, J. |
| Copyright Year | 1974 |
| Description | A ring R is called a qc-ring if each cyclic R-module is quasi-injective. For various properties of these rings we refer to Ahsan (1) and Koehler (15). In this paper we shall obtain some additional results related to qc-rings. The scheme of the paper is as follows. Section 2 contains various preliminary definitions and results. In Section 3, we shall prove that every commutative hypercyclic ring is a qc-ring. In this section, we shall also show that a qc-ring which satisfies the ascending chain condition on its annihilators has nilpotent Jacobson-radical. Finally, in Section 4, we shall study rings all of whose proper factor rings are qc. Such rings will be called “ restricted qc ”. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3D9F24488A3819CAC2E8EBE11347892A/S0013091500010269a.pdf/div-class-title-on-rings-with-quasi-injective-cyclic-modules-div.pdf |
| Ending Page | 145 |
| Page Count | 7 |
| Starting Page | 139 |
| ISSN | 00130915 |
| e-ISSN | 14643839 |
| DOI | 10.1017/s0013091500010269 |
| Journal | Proceedings of the Edinburgh Mathematical Society |
| Issue Number | 2 |
| Volume Number | 19 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1974-09-01 |
| Access Restriction | Open |
| Subject Keyword | Proceedings of the Edinburgh Mathematical Society Qc Ring |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
