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PARTIAL ORDERS ON PARTIAL BAER–LEVI SEMIGROUPS
| Content Provider | Scilit |
|---|---|
| Author | Singha, Boorapa Sanwong, Jintana Sullivan, R. P. |
| Copyright Year | 2010 |
| Description | Marques-Smith and Sullivan [‘Partial orders on transformation semigroups’, Monatsh. Math.140 (2003), 103–118] studied various properties of two partial orders on P(X), the semigroup (under composition) consisting of all partial transformations of an arbitrary set X. One partial order was the ‘containment order’: namely, if α,β∈P(X) then α⊆β means xα=xβ for all x∈dom α, the domain of α. The other order was the so-called ‘natural order’ defined by Mitsch [‘A natural partial order for semigroups’, Proc. Amer. Math. Soc.97(3) (1986), 384–388] for any semigroup. In this paper, we consider these and other orders defined on the symmetric inverse semigroup I(X) and the partial Baer–Levi semigroup PS(q). We show that there are surprising differences between the orders on these semigroups, concerned with their compatibility with respect to composition and the existence of maximal and minimal elements. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/84973060A5AE48403039E7597D2971C8/S0004972709001038a.pdf/div-class-title-partial-orders-on-partial-baer-levi-semigroups-div.pdf |
| Ending Page | 207 |
| Page Count | 13 |
| Starting Page | 195 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972709001038 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 2 |
| Volume Number | 81 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2010-04-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Primary 20m20 Secondary 04a05 Partial Transformation Semigroup Baer–levi Semigroup Natural Partial Order Maximal (minimal) Element |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
