Timeline for Countably infinite monoids with minimal right ideals
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 13, 2022 at 19:59 | comment | added | khers | @Benjamin Steinberg Thanks so much | |
| Jul 13, 2022 at 19:10 | comment | added | Benjamin Steinberg | I think you can find some stuff on this in Clifford and Preston's classic book on semigroup theory. They call it the minimum condition on right ideals. | |
| Jul 13, 2022 at 18:59 | comment | added | khers | @Benjamin Steinberg Thanks again, is there any reference about semigroups with descending chain condition on right ideals? | |
| Jul 13, 2022 at 17:30 | comment | added | Benjamin Steinberg | Asking for classes with this property is more hopeful than asking for a classification. Any monoid with descending chain condition on right ideals (e.g. finite monoids) has it, but there are many other ways to get them like artificially adding a 0. | |
| Jul 13, 2022 at 14:25 | comment | added | khers | @Benjamin Steinberg Thanks for the guidance! For example, all commutative artinian monoids have this property. I want to know the other classes of monoids with this property and you kindly introduced me two new families. | |
| Jul 13, 2022 at 13:01 | comment | added | Benjamin Steinberg | And all finite or compact monoids have minimal right ideals. | |
| Jul 13, 2022 at 13:01 | comment | added | Benjamin Steinberg | What would you hope to mean by a classifications? You can take any countable monoid and adjoin a zero to get a minimal right ideal. | |
| Jul 13, 2022 at 8:04 | history | asked | khers | CC BY-SA 4.0 |