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- W2113222278 abstract "Analogous to left p.q.-Baer property of a ring [G. F. Birkenmeier, J. Y. Kim and J. K. Park, Principally quasi-Baer rings, Comm. Algebra29 (2001) 639–660], we say a right R-module M is endo-principallyquasi-Baer (or simply, endo-p.q.-Baer) if for every m ∈ M, l S (Sm) = Se for some e 2 = e ∈ S = End R (M). It is shown that every direct summand of an endo-p.q.-Baer module inherits the property that any projective (free) module over a left p.q.-Baer ring is an endo-p.q.-Baer module. In particular, the endomorphism ring of every infinitely generated free right R-module is a left (or right) p.q.-Baer ring if and only if R is quasi-Baer. Furthermore, every principally right ℱℐ-extending right ℱℐ-𝒦-nonsingular ring is left p.q.-Baer and every left p.q.-Baer right ℱℐ-𝒦-cononsingular ring is principally right ℱℐ-extending." @default.
- W2113222278 created "2016-06-24" @default.
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- W2113222278 date "2015-10-06" @default.
- W2113222278 modified "2023-09-26" @default.
- W2113222278 title "Endo-principally quasi-Baer modules" @default.
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- W2113222278 doi "https://doi.org/10.1142/s0219498815501327" @default.
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