FP-injective objects in the category of N-complexes

Bo Lu ()
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Bo Lu: Northwest Minzu University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 242-255

Abstract: Abstract We show that an N-complex of modules C is FP-injective if and only if C is N-exact and $$\textrm{Z}_n^i(C)$$ Z n i ( C ) is an FP-injective module for each $$i=1,2,\cdots ,N$$ i = 1 , 2 , ⋯ , N and each $$n\in \mathbb {Z}$$ n ∈ Z by virtue of Gaussian binomial coefficients. Applications of this result go in three directions. Firstly, over a coherent ring, we prove that a bounded above N-complex C is FP-injective if and only if C is N-exact and $$C_n$$ C n is an FP-injective module for each $$n\in \mathbb {Z}$$ n ∈ Z . Secondly, we obtain some examples of FP-injective N-complexes for some fixed integer N. Finally, we give a characterization of coherent rings.

Keywords: Finitely presented N-complex; FP-injective N-complex; FP-injective module; Coherent ring; 18G25; 18G35 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-022-00360-4

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