Rings whose modules are finitely generated over their endomorphism rings

• Autorzy: Nguyen Viet Dung , José Luis García
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation
• 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
• 16G10: Representations of Artinian rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 114
• Numer: 2
• Strony: 155-176

Daty

wydano

2009

Twórcy

autor

Nguyen Viet Dung

• Department of Mathematics, Ohio University-Zanesville, Zanesville, OH 43701, U.S.A.

autor

José Luis García

• Department of Mathematics, University of Murcia, 30100 Espinardo, Murcia, Spain

Identyfikatory

DOI

10.4064/cm114-2-1