Volume 31, Issue 4
On Weakly P.P. Rings

Commun. Math. Res., 31 (2015), pp. 362-372.

Published online: 2021-05

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• Abstract

We introduce, in this paper, the right weakly p.p. rings as the generalization of right p.p. rings. It is shown that many properties of the right p.p. rings can be extended onto the right weakly p.p. rings. Relative examples are constructed. As applications, we also characterize the regular rings and the semisimple rings in terms of the right weakly p.p. rings.

• Keywords

weakly p.p. ring, $GP$-injective module, regular ring.

16D40, 16E50

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@Article{CMR-31-362, author = {Yueming and Xiang and and 18755 and and Yueming Xiang and Ouyang and Lunqun and and 18756 and and Ouyang Lunqun and Shugui and Wang and and 18758 and and Shugui Wang}, title = {On Weakly P.P. Rings}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {4}, pages = {362--372}, abstract = {

We introduce, in this paper, the right weakly p.p. rings as the generalization of right p.p. rings. It is shown that many properties of the right p.p. rings can be extended onto the right weakly p.p. rings. Relative examples are constructed. As applications, we also characterize the regular rings and the semisimple rings in terms of the right weakly p.p. rings.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.04.08}, url = {http://global-sci.org/intro/article_detail/cmr/18918.html} }
TY - JOUR T1 - On Weakly P.P. Rings AU - Xiang , Yueming AU - Lunqun , Ouyang AU - Wang , Shugui JO - Communications in Mathematical Research VL - 4 SP - 362 EP - 372 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.04.08 UR - https://global-sci.org/intro/article_detail/cmr/18918.html KW - weakly p.p. ring, $GP$-injective module, regular ring. AB -

We introduce, in this paper, the right weakly p.p. rings as the generalization of right p.p. rings. It is shown that many properties of the right p.p. rings can be extended onto the right weakly p.p. rings. Relative examples are constructed. As applications, we also characterize the regular rings and the semisimple rings in terms of the right weakly p.p. rings.

Yueming Xiang, Lunqun Ouyang & Shugui Wang. (2021). On Weakly P.P. Rings. Communications in Mathematical Research . 31 (4). 362-372. doi:10.13447/j.1674-5647.2015.04.08
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