Stable equivalence of uniserial rings

Fuller, K. R.; Haack, J.; Hullinger, H.

doi:10.1090/S0002-9939-1978-0463231-9

Stable equivalence of uniserial rings
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by K. R. Fuller, J. Haack and H. Hullinger PDF

Proc. Amer. Math. Soc. 68 (1978), 153-158 Request permission

Abstract:

It is well known that two basic rings are Morita equivalent if and only if they are isomorphic. Here it is shown that local uniserial rings are stably equivalent in the sense of M. Auslander and I. Reiten in case they are isomorphic modulo certain powers of their radicals. In particular, two commutative local uniserial rings of Loewy length n are stably equivalent if and only if they are isomorphic modulo the [n/2]th power of their radicals.

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