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On FF-rings. (English) Zbl 1239.13002

The authors study the class of rings in which every flat ideal is finitely generated (for short, FF-rings; see also J. D. Sally and W. V. Vasconcelos, Commun. Algebra 3, 531–543 (1975; Zbl 0315.13010)]. In particular, they investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as direct products, pullback rings, and trivial ring extensions (or idealizations). Their results generate examples which enrich the current literature with new and original families of non-Noetherian rings that satisfy this property.

MSC:

13A15 Ideals and multiplicative ideal theory in commutative rings
13C10 Projective and free modules and ideals in commutative rings
13C11 Injective and flat modules and ideals in commutative rings
13B02 Extension theory of commutative rings
13D07 Homological functors on modules of commutative rings (Tor, Ext, etc.)

Citations:

Zbl 0315.13010
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References:

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