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- Title
On certain semigroups of transformations with restricted range.
- Authors
Li, De Biao; Zhang, Wen Ting; Luo, Yan Feng
- Abstract
Let X = { 1 , ... , n } be a finite chain and let ℐ (X) be the semigroup of all injective order-preserving partial transformations on X. For any nonempty subset Y of X , let ℐ (X , Y) be the subsemigroup of ℐ (X) of all transformations with range contained in Y. In this paper, we characterize Green's relations on ℐ (X , Y) , and show that the semigroup ℐ (X , Y) is left abundant but not right abundant when Y is a proper subset of X. Moreover, the cardinality and the rank of the semigroup ℐ (X , Y) is determined.
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 7, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823501438