Displaying similar documents to “ E -rings and differential polynomials over universal fields”

Embedding torsionless modules in projectives.

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.

Perfect rings for which the converse of Schur's lemma holds.

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.

Right Utumi p.p.-rings

Ulrich Albrecht (2010)

Rendiconti del Seminario Matematico della Università di Padova

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