Abstract
Let [n] = {1, 2, …, n} be a őnite chain and let Pn (resp., Tn ) be the semigroup of partial transformations on [n] (resp., full transformations on [n]). Let CPn = {α ∈ Pn: (for all x, y ∈Domα) |xα − yα| ⩽ |x − y|} (resp., CTn = {α ∈ Tn: (for all x, y ∈ [n]) |xα−yα| ⩽ |x−y|} ) be the subsemigroup of partial contraction mappings on [n] (resp., subsemigroup of full contraction mappings on [n]). We characterize all the starred Green’s relations on CPn and it subsemigroup of order preserving and/or order reversing and subsemigroup of order preserving partial contractions on [n], respectively. We show that the semigroups CPn and CTn, and some of their subsemigroups are left abundant semigroups for all n but not right abundant for n ⩾ 4. We further show that the set of regular elements of the semigroup CTn and its subsemigroup of order preserving or order reversing full contractions on [n], each forms a regular subsemigroup and an orthodox semigroup, respectively.
Original language | English |
---|---|
Pages (from-to) | 299-320 |
Number of pages | 22 |
Journal | Algebra and Discrete Mathematics |
Volume | 32 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2021 |
Externally published | Yes |
Keywords
- orthodox semigroups
- quasiadequate semigroups
- regularity
- starred Green’s relations
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics