Rings with flat socles

Xiao, Yu Fei

doi:10.1090/S0002-9939-1995-1254860-3

Rings with flat socles
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Proc. Amer. Math. Soc. 123 (1995), 2391-2395 Request permission

Abstract:

We show that the class of rings with flat socles is closed under the formation of polynomial extensions, direct products, and excellent extensions. We also point out that if a ring R can be embedded into a semisimple Artinian ring, then all finitely generated flat R-modules are projective.

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On rings whose flat cyclic modules are projective