Timeline for An alternative definition for finitely generated (and principal) ideals in a semigroup
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 28 at 2:56 | comment | added | Salvo Tringali | In the commutative case (where the two definitions agree), $\mathfrak I_{\rm fin}(S)$ has been extensively studied by people in multiplicative ideal theory as an important special case of a (weak) ideal system. With that said, one could always define $\mathfrak I_{\rm fin}(S)$ as the subsemigroup of the ideal semigroup generated by the ideals that are finitely generated in the usual sense. In hindsight, I'm more or less convinced that this would be more natural than adopting the alternative definition of 'finitely generated ideal' suggested in the OP. | |
| Mar 20 at 14:53 | comment | added | Benjamin Steinberg | The finitely generated case is more reasonable but I don't think very studied | |
| Mar 20 at 14:40 | comment | added | Salvo Tringali | I don't disagree. However, there are instances where the semigroup of (two-sided) ideals, which are finitely generated both as left and as right ideals, is sufficiently large to encode a significant fragment of the structure of the original semigroup. And that's where my motivation comes from. | |
| Mar 20 at 11:43 | comment | added | Benjamin Steinberg | I’ve not seen it. I think it very rare for an ideal to be principal as both a left and right ideal in general. | |
| Mar 20 at 8:39 | history | edited | Salvo Tringali | CC BY-SA 4.0 |
fixed a couple of mistakes
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| Mar 20 at 6:26 | history | edited | Salvo Tringali | CC BY-SA 4.0 |
deleted 14 characters in body
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| Mar 20 at 6:20 | history | asked | Salvo Tringali | CC BY-SA 4.0 |