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( n , d ) -injective covers, n -coherent rings, and ( n , d ) -rings

Weiqing Li, Baiyu Ouyang (2014)

Czechoslovak Mathematical Journal

It is known that a ring R is left Noetherian if and only if every left R -module has an injective (pre)cover. We show that ( 1 ) if R is a right n -coherent ring, then every right R -module has an ( n , d ) -injective (pre)cover; ( 2 ) if R is a ring such that every ( n , 0 ) -injective right R -module is n -pure extending, and if every right R -module has an ( n , 0 ) -injective cover, then R is right n -coherent. As applications of these results, we give some characterizations of ( n , d ) -rings, von Neumann regular rings and semisimple rings....

(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras

Chao Wang, Xiao Yan Yang (2017)

Czechoslovak Mathematical Journal

Let Λ = A M 0 B be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective Λ -modules under the condition that M is a cocompatible ( A , B ) -bimodule, we establish a recollement of the stable category Ginj ( Λ ) ¯ . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over Λ .

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