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Paper IPM / M / 16698 |
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Abstract: | |
We introduce and study the notion of ES-w-stability for an integral domain R. A nonzero ideal I of R is called ES-w-stable if (I^2)_w = (JI)_w for some t-invertible ideal J of R contained in I, and I is called weakly ES-w-stable if I_w = (JE)_w for some t-invertible fractional ideal J of R and w-idempotent fractional ideal E of R. We define R to be an ES-w-stable domain
(resp., a weakly ES-w-stable domain) if every nonzero ideal of R is ES-w-stable (resp., weakly ES-w-stable). These notions allow us to generalize some well-known properties of ES-stable and weakly ES-stable domains.
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