University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 35 4 2024 10 01 On Projection Invariant Rickart Modules 321 328 104292 10.22059/jsciences.2025.379598.1007873 EN Yaser Maleki 1 Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran 0000-0003-4012-7738 Ahmad Moussavi 1 Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran 0000-0002-7775-9782 Yeliz Kara Bursa Uludag University, Faculty of Arts and Science, Department of Mathematics, 16059 Gorukle, Bursa/TURKEY Journal Article 2024 07 25 This study examined π-Rickart modules, a module-theoretic analog of π-Rickart rings, from the perspective of their endomorphism rings. It is shown that π-Rickart conditions are located between π-e. Baer and p.q.-Baer conditions, and it is established that the corresponding endomorphism ring possesses the appropriate π-Rickart property. Besides, the notion of π-e.AIP modules is presented. Furthermore, connections to the aforementioned concepts of π-Rickart, endo-AIP, and π-e.AIP modules are examined. https://jsciences.ut.ac.ir/article_104292_a00448af12a60bcbff48b1a698280558.pdf