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Gorenstein injective dimension for complexes and Iwanaga-Gorenstein rings. (English) Zbl 1106.13024

Motivated by the work of O. Veliche [Trans. Am. Math. Soc. 358, No. 3, 1257–1283 (2006; Zbl 1094.16007)], the author extends the concept of Gorenstein injective dimension to the setting of unbounded complexes over associative rings and presents some its applications. In particular, some new characterizations of Iwanaga-Gorenstein rings in terms of the class of complexes of finite Gorenstein injective dimension and also in terms of the interplay between same class and the class of complexes of finite projective Gorenstein dimension are provided.

MSC:

13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
13D05 Homological dimension and commutative rings
55N35 Other homology theories in algebraic topology

Citations:

Zbl 1094.16007
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References:

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