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Principally π-Baer rings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 20 فروردین 1404 اصل مقاله (438.4 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34744.5196 | ||
| نویسندگان | ||
| Somayeh Moradi1؛ Hamid Haj Seyyed Javadi* 1؛ Ahmad Moussavi2 | ||
| 1Department of Mathematics and Computer Science, Shahed University, Tehran, Iran | ||
| 2Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran | ||
| تاریخ دریافت: 24 تیر 1403، تاریخ پذیرش: 12 آذر 1403 | ||
| چکیده | ||
| We say a ring is right principally $\pi$-Baer (or simply right $p.\pi$-Baer) if an idempotent generates the right annihilator of every projection invariant principal left ideal. The class of right $p.\pi$-Baer rings includes the von Neumann regular rings (and hence right p.p-rings) and all $\pi$-Baer rings. This class of rings is closed under direct products. The behavior of the right $p.\pi$-Baer condition is investigated concerning various constructions and extensions. Moreover, we extend a theorem of Kist for commutative p.p-rings to right $p.\pi$-Baer rings for which every prime ideal contains a unique minimal prime ideal without using topological arguments. | ||
| کلیدواژهها | ||
| p.p ring؛ Baer ring؛ quasi-Baer ring؛ principally quasi-Baer ring؛ π-Baer ring؛ p.π-Baer ring؛ semicentral idempotent | ||
| مراجع | ||
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