Cotilting modules over commutative Noetherian rings

Jan Trlifaj; Dolors Herbera; Jan Šťovíček

doi:10.1016/j.jpaa.2014.01.008

Cotilting modules over commutative Noetherian rings

Jan Trlifaj, Dolors Herbera, Jan Šťovíček

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Recentment, les classes de inclinació i cotiltació sobre els anells Noetherians commutatius s'han classificat a [2]. Procedim i construïm un mòdul n-cotilting que indueix C per una iteració d'injectius precovers. Un refinament addicional de la construcció produeix el mòdul n-cotilting mínim únic que indueix C. Finalment, considerem la localització: un mòdul cotiling es diu ampli si totes les seves localitzacions són cotiltades. Provem que per a cada classe 1-cotilting hi ha un mòdul ample que ho indueix, però donem un exemple d'una classe 2-cotilting que falla aquesta propietat. © 2014 Elsevier B.V.

Idioma original	Anglès
Pàgines (de-a)	1696-1711
Revista	Journal of Pure and Applied Algebra
Volum	218
Número	9
DOIs	https://doi.org/10.1016/j.jpaa.2014.01.008
Estat de la publicació	Publicada - 1 de gen. 2014

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abstract = "Recently, tilting and cotilting classes over commutative Noetherian rings have been classified in [2]. We proceed and, for each n-cotilting class C, construct an n-cotilting module inducing C by an iteration of injective precovers. A further refinement of the construction yields the unique minimal n-cotilting module inducing C. Finally, we consider localization: a cotilting module is called ample, if all of its localizations are cotilting. We prove that for each 1-cotilting class, there exists an ample cotilting module inducing it, but give an example of a 2-cotilting class which fails this property. {\textcopyright} 2014 Elsevier B.V.",

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AU - Trlifaj, Jan

AU - Herbera, Dolors

AU - Šťovíček, Jan

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N2 - Recently, tilting and cotilting classes over commutative Noetherian rings have been classified in [2]. We proceed and, for each n-cotilting class C, construct an n-cotilting module inducing C by an iteration of injective precovers. A further refinement of the construction yields the unique minimal n-cotilting module inducing C. Finally, we consider localization: a cotilting module is called ample, if all of its localizations are cotilting. We prove that for each 1-cotilting class, there exists an ample cotilting module inducing it, but give an example of a 2-cotilting class which fails this property. © 2014 Elsevier B.V.

AB - Recently, tilting and cotilting classes over commutative Noetherian rings have been classified in [2]. We proceed and, for each n-cotilting class C, construct an n-cotilting module inducing C by an iteration of injective precovers. A further refinement of the construction yields the unique minimal n-cotilting module inducing C. Finally, we consider localization: a cotilting module is called ample, if all of its localizations are cotilting. We prove that for each 1-cotilting class, there exists an ample cotilting module inducing it, but give an example of a 2-cotilting class which fails this property. © 2014 Elsevier B.V.

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Cotilting modules over commutative Noetherian rings

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