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Rings whose modules are finitely generated over their endomorphism rings

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Dung N., García J.

Colloquium Mathematicum

2009

tom 114

nr 2

155-176

A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the following conditions are equivalent: (a) Every right R-module is finendo; (b) Every left R-module is cofinendo; (c) R is left pure semisimple and every finitely generated indecomposable left R-module is cofinendo; (d) R is left pure semisimple and every finitely generated indecomposable left R-module is finendo; (e) R is of finite representation type. Moreover, if R is an arbitrary ring, then (a) ⇒ (b) ⇔ (c), and any ring R satisfying (c) has a right Morita duality.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Dung N.

1 García J.

1 2009

Wyniki wyszukiwania

Rings whose modules are finitely generated over their endomorphism rings