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Construction of regular semigroups with inverse transversals
| Content Provider | Scilit |
|---|---|
| Author | Saito, Tatsuhiko |
| Copyright Year | 1989 |
| Description | Let S be a regular semigroup. An inverse subsemigroup S° of S is an inverse transversal if |V(x)∩S°| = 1 for each x∈S, where V(x) denotes the set of inverses of x. In this case, the unique element of V(x)∩S° is denoted by x°, and x°° denotes $(x°)^{–1}$. Throughout this paper S denotes a regular semigroup with an inverse transversal S°, and E(S°) = E° denotes the semilattice of idempotents of S°. The sets {e∈S:ee° = e} and {f∈S:f°f=f} are denoted by $I_{s}$ and $Λ_{s}$, respectively, or simply I and Λ. Though each element of these sets is idempotent, they are not necessarily sub-bands of S. When both I and Λ are sub-bands of S, S° is called an S-inverse transversal. An inverse transversal S° is multiplicative if x°xyy°∈E°, and S° is weakly multiplicative if (x°xyy°)°∈E° for every x, y∈S. A band B is left [resp. right] regular if e f e = e f [resp. e f e = f e], and B is left [resp. right] normal if e f g = e g f [resp. e f g = f e g] for every e, f, g∈B. A subset Q of S is a quasi-ideal of S if QSQ ⊆ S. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E5AB73F66EFCB30F92AB2F70C592C0B6/S0013091500006891a.pdf/div-class-title-construction-of-regular-semigroups-with-inverse-transversals-div.pdf |
| Ending Page | 51 |
| Page Count | 11 |
| Starting Page | 41 |
| ISSN | 00130915 |
| e-ISSN | 14643839 |
| DOI | 10.1017/s0013091500006891 |
| Journal | Proceedings of the Edinburgh Mathematical Society |
| Issue Number | 1 |
| Volume Number | 32 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1989-02-01 |
| Access Restriction | Open |
| Subject Keyword | Proceedings of the Edinburgh Mathematical Society Regular Semigroup Inverse Transversal |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
