New orders in primitive inverse semigroups
We introduce the following variant of an order and semigroup of quotients in inverse semigroups. A subsemigroup S of an inverse semigroup Q is a new left order in Q if for every q £ Q, there exist a,b £ S such that q = a~1b. Here a - 1 is the unique inverse of a in Q. A new right order is defined du...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2015
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| Sorozat: | Acta scientiarum mathematicarum
81 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| mtmt: | http://dx.doi.org/10.14232/actasm-013-040-7 |
| Online Access: | http://acta.bibl.u-szeged.hu/35197 |
| Tartalmi kivonat: | We introduce the following variant of an order and semigroup of quotients in inverse semigroups. A subsemigroup S of an inverse semigroup Q is a new left order in Q if for every q £ Q, there exist a,b £ S such that q = a~1b. Here a - 1 is the unique inverse of a in Q. A new right order is defined dually, and a new order is the conjunction of the two. This concept produces more (left, right) orders in an inverse semigroup than those studied heretofore. A primitive inverse semigroup is a nontrivial inverse semigroup with zero in which all nonzero idempotents are primitive. It can best be characterized as an orthogonal sum of Brandt semigroups. Our main result consists of necessary and sufficient conditions on a semigroup S to be a new left order in a Brandt semigroup. They are five in number and of relatively concrete form. This result (with a long proof) is used to give two characterizations of new orders in Brandt semigroups, and eventually to perform a similar analysis for the same kinds of orders in primitive inverse semigroups. A uniqueness result concludes the work. |
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| Terjedelem/Fizikai jellemzők: | 111-131 |
| ISSN: | 0001-6969 |