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Gorenstein Homological Aspects of Monomorphism Categories via Morita Rings

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Abstract

In this paper we construct Gorenstein-projective modules over Morita rings with zero bimodule homomorphisms and we provide sufficient conditions for such rings to be Gorenstein Artin algebras. This is the first part of our work which is strongly connected with monomorphism categories. In the second part, we investigate monomorphisms where the domain has finite projective dimension. In particular, we show that the latter category is a Gorenstein subcategory of the monomorphism category over a Gorenstein algebra. Finally, we consider the category of coherent functors over the stable category of this Gorenstein subcategory and show that it carries a structure of a Gorenstein abelian category.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Nan Gao

  2. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, 7491, Norway

    Chrysostomos Psaroudakis

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  1. Nan Gao
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  2. Chrysostomos Psaroudakis
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Correspondence to Chrysostomos Psaroudakis.

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Presented by Jon F. Carlson.

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Gao, N., Psaroudakis, C. Gorenstein Homological Aspects of Monomorphism Categories via Morita Rings. Algebr Represent Theor 20, 487–529 (2017). https://doi.org/10.1007/s10468-016-9652-1

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