On \(n\)-coherent rings. (English) Zbl 0877.16010

Let \(R\) be a ring. D. L. Costa [Commun. Algebra 22, No. 10, 3997-4011 (1994; Zbl 0814.13010)] introduced the concepts of \(n\)-presented modules and left \(n\)-coherent rings for a nonnegative integer \(n\). A left \(R\)-module \(M\) is \(n\)-presented if there is an exact sequence \(F_n\to F_{n-1}\to\dots\to F_1\to F_0\to M\to 0\) with each \(F_i\) finitely generated and free. Then \(R\) is called left \(n\)-coherent if every \(n\)-presented left \(R\)-module is \((n+1)\)-presented. The authors show that many of the usual characterizations of a left coherent ring have analogues for the left \(n\)-coherent ring case.


16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras)


Zbl 0814.13010
Full Text: DOI


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