### On commutative FGI-Rings.

M. Barry, C. T. Gueye, M. Sanghare (1997)

Extracta Mathematicae

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M. Barry, C. T. Gueye, M. Sanghare (1997)

Extracta Mathematicae

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James Osterburg (1979)

Czechoslovak Mathematical Journal

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Jan Žemlička, Jan Trlifaj (1997)

Rendiconti del Seminario Matematico della Università di Padova

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Publicacions Matemàtiques

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Zelmanowitz [12] introduced the concept of ring, which we call ^{⊥} of a subset X of R is zero, then X_{1}
^{⊥} = 0 for a finite subset X_{1} ⊆ X.
(ZIP 2) If L is a left ideal and if L^{⊥} = 0, then L_{1}
...

Sanghare, Mamadou (1997)

International Journal of Mathematics and Mathematical Sciences

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Beiträge zur Algebra und Geometrie

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International Journal of Mathematics and Mathematical Sciences

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In this paper we study a condition right FGTF on a ring R, namely when all finitely generated torsionless right R-modules embed in a free module. We show that for a von Neuman regular (VNR) ring R the condition is equivalent to every matrix ring R is a Baer ring; and this is right-left symmetric. Furthermore, for any Utumi VNR, this can be strengthened: R is FGTF iff R is self-injective.