Abstract
Let Dn (script O signn) be the semigroup of all finite order-decreasing (order-preserving) full transformations of an n-element chain, and let D(n,r) = {α ∈ Dn : |Im α| ≤ r} (C(n,r) = D(n,r) ∩ script O signn) be the two-sided ideal of Dn (Dn ∩ script O signn). Then it is shown that for r ≥ 2, the Rees quotient semigroup DPr(n) = D(n,r)/D(n,r-1) (CPr(n) = C(n,r)/C(n,r- 1)) is an R-trivial ( J-trivial) idempotent-generated 0*-bisimple primitive abundant semigroup. The order of CPr(n) is shown to be 1 + (n-1 r-1) ( nr ) /(n - r + 1). Finally, the rank and idempotent ranks of CPr(n) (r < n) are both shown to be equal to ( n-1r-1 ).
Original language | English |
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Pages (from-to) | 184-200 |
Number of pages | 17 |
Journal | Semigroup Forum |
Volume | 69 |
Issue number | 2 |
DOIs | |
Publication status | Published - Sept 2004 |
Externally published | Yes |
ASJC Scopus subject areas
- Algebra and Number Theory