### The Armendariz module and its application to the Ikeda-Nakayama module.

Koşan, M.Tamer (2006)

International Journal of Mathematics and Mathematical Sciences

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Koşan, M.Tamer (2006)

International Journal of Mathematics and Mathematical Sciences

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Abdelfattah Haily, Mostafa Alaoui (2001)

Publicacions Matemàtiques

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If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones.

Carl Faith (1990)

Publicacions Matemàtiques

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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.

Radhey S. Singh, Renu Shrivastava (1992)

Czechoslovak Mathematical Journal

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Jan Trlifaj (1982)

Commentationes Mathematicae Universitatis Carolinae

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Zaks, Abraham (1973)

Portugaliae mathematica

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Antonio García Rodicio (1987)

Extracta Mathematicae

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Mahdou, Najib (2006)

International Journal of Mathematics and Mathematical Sciences

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Al-Ezeh, H. (1987)

International Journal of Mathematics and Mathematical Sciences

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