Geodesic
On $p$-injectivity, YJ-injectivity and quasi-Frobeniusean rings
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 1, pp. 33-42

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A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms of $p$-injectivity. Also, a commutative YJ-injective ring with maximum condition on annihilators and finitely generated socle is quasi-Frobeniusean.
Classification : 16D30, 16D36, 16D50, 16E50, 16L60, 16N60, 16P20
Keywords: von Neumann regular; $V$-ring; Artinian ring; $p$-injectivity; YJ-injectivity; quasi-Frobeniusean 
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     author = {Yue Chi Ming, Roger},
     title = {On $p$-injectivity, {YJ-injectivity} and {quasi-Frobeniusean} rings},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {33--42},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {2002},
     mrnumber = {1903305},
     zbl = {1068.16004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002__43_1_a3/}
}
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Yue Chi Ming, Roger. On $p$-injectivity, YJ-injectivity and quasi-Frobeniusean rings. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 1, pp. 33-42. http://geodesic.mathdoc.fr/item/CMUC_2002__43_1_a3/