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- W2244574811 abstract "A noetherian ring R satisfies the descending chain condition on two-sided ideals (“is bi-artinian”) if and only if, for each prime P ∈ spec( R ), R/P has a unique minimal ideal (necessarily idempotent and left-right essential in R/P ). The analogous statement for merely right noetherian rings is false, although our proof does not use the full noetherian condition on both sides, requiring only that two-sided ideals be finitely generated on both sides and that R/Q be right Goldie for each Q ∈ spec(R) . Examples exist, for each n ∈ℕ and in all characteristics, of bi-artinian noetherian domains D n with composition series of length 2 n and with a unique maximal ideal of height n . Noetherian rings which satisfy the related E-restricted bi-d.c.c. do not, in general, satisfy the second layer condition (on either side), but do satisfy the Jacobson conjecture." @default.
- W2244574811 created "2016-06-24" @default.
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- W2244574811 date "2001-01-01" @default.
- W2244574811 modified "2023-09-26" @default.
- W2244574811 title "Bi-artinian noetherian rings" @default.
- W2244574811 doi "https://doi.org/10.1017/s0017089501010023" @default.
- W2244574811 hasPublicationYear "2001" @default.
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