On modules with piecewise-Koszul towers

• Autores: Jia-feng Lü
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 35, Nº 1, 2009, págs. 185-207
• Idioma: inglés
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• Resumen

  • The concept of (strongly) weakly piecewise-Koszul module is introduced. Let A be a piecewise-Koszul algebra and M a finitely generated graded A-module. Then M is weakly piecewise-Koszul if and only if M admits a tower of piecewise-Koszul modules. As applications of the approximation chain, we show that the finitistic dimension conjecture is true in the category of weakly piecewise-Koszul modules, and if M is (strongly) weakly piecewise-Koszul, then the Koszul dual of M is not only finitely generated, but also generated in degree zero. In particular, if M is perfect, then M is strongly piecewise-Koszul if and only if the Koszul dual of M is finitely generated and generated in degree zero. Furthermore, we show that M is weakly piecewise-Koszul if and only if the Koszul dual of G(M) is finitely generated and generated in degree zero.