Finitistic n-Self-Cotilting Modules

Abstract

We study a class of modules which can be characterized using a duality theorem, called finitistic n-self-cotilting. Such a module Q can be characterized using dual conditions of some generalizations for star modules: every module M which has a right resolution with n terms isomorphic to finite powers of Q (i.e., M is n-finitely Q-copresented) has a right resolution with (n + 1) terms, and the functor Hom _R (−, Q) preserves the exactness of all monomorphisms with their ranges finite powers of Q and cokernels n-finitely Q-copresented modules. In the general case, these modules are independent toward other kinds of modules which are characterized using some dualities (w-Π _f -quasi injective modules, costar modules, f-cotilting modules). Closure properties for the classes involved in the duality are studied. At the end of the article, connections with the cotilting theory are exhibited, in the case of finitely dimensional algebras over fields.

Key Words:

• n-Cotilting module
• Duality
• n-Finitely Q-copresented module
• Resolving class

2000 Mathematics Subject Classification:

• 16D90 (16E30)

ACKNOWLEDGMENTS

I like to thank Professors Lidia Angeleri Hügel, Jan Trlifaj, and Robert Wisbauer for their useful critical remarks.

The author is supported by the grant PN2_ID_489 (CNCSIS).

Notes

¹Added in proof: The ℤ-module ℚ is also a ☆²-module which is not finitely generated, hence the answer for [19, Question 2] is negative.

Communicated by R. Wisbauer.