On \(n\)-coherent rings, \(n\)-hereditary rings and \(n\)-regular rings. (English) Zbl 1277.16007

Summary: We observe some new characterizations of \(n\)-presented modules. Using the concepts of \((n,0)\)-injectivity and \((n,0)\)-flatness of modules, we also present some characterizations of right \(n\)-coherent rings, right \(n\)-hereditary rings, and right \(n\)-regular rings.


16D80 Other classes of modules and ideals in associative algebras
16D40 Free, projective, and flat modules and ideals in associative algebras
16D50 Injective modules, self-injective associative rings
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
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)