Some precovers and preenvelopes in functor categories

Zongyang Xie () and Zhongkui Liu ()
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Zongyang Xie: Northwest Normal University
Zhongkui Liu: Northwest Normal University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 3, 903-910

Abstract: Abstract Let $$n\ge 1$$ n ≥ 1 be an integer. A functor $$F\in $$ F ∈ (mod-R, Ab) is called n-strongly FP -injective if F is isomorphic to some functor $$-\otimes M$$ - ⊗ M in (mod-R, Ab) with M an $$FP_n$$ F P n -injective left R-module. A functor $$G\in $$ G ∈ ((mod-R) $$^{\text{ op }}$$ op , Ab) is said to be n-strongly flat if G is isomorphic to some functor $$(-,N)$$ ( - , N ) in ((mod-R) $$^{\text{ op }}$$ op , Ab) with N an $$FP_n$$ F P n -flat right R-module. Precovers and preenvelopes by n-strongly FP-injective and n-strongly flat functors are investigated over a general ring. As applications, special rings are characterized in terms of this two classes of functors.

Keywords: n-strongly FP-injective functor; $$FP_n$$ F P n -injective; n-strongly flat functor; $$FP_n$$ F P n -flat modules; (pre)cover; (pre)envelope; 16B50; 18A25; 18G05; 18G25 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00094-9

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