Relative global dimensions of extensions |
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| Authors: | Shufeng Guo |
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| Institution: | 1. Faculty of Science, Guilin University of Aerospace Technology, Guilin, China;2. School of Mathematical Sciences, Capital Normal University, Beijing, China |
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| Abstract: | An extension of algebras is a homomorphism of algebras preserving identities. Given an extension f:B→A, the relative global dimension of f is defined to be the supremum of relative projective dimensions of all A-modules. In this paper, we compare relative homological dimensions of two extensions of ordinary algebras under certain conditions. As an application, for any natural number n, we present a general method for constructing non-trivial extensions of Artin algebras of relative global dimension at least n. |
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| Keywords: | Artin algebra constructions of extensions relative global dimension relatively projective module |
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