On Rank Properties of Endomorphisms of Finite Circular Orders

REFERENCES

• Araújo , J. ( 2003 ). Idempotent generated endomorphisms of an independence algebra . Semigroup Forum 67 : 464 – 467 . [CSA]
   Web of Science ®Google Scholar
• Araújo , J. , Mitchell , J. D. ( 2005 ). An elementary proof that every singular matrix is a product of idempotent matrices . Amer. Math. Monthly 112 : 641 – 645 . [CSA]
   Web of Science ®Google Scholar
• Arthur , R. E. , Ruškuc , N. ( 2000 ). Presentations for two extensions of the monoid of order-preserving mappings on a finite chain . Southeast Asian Bull. Math. 24 : 1 – 7 . [CSA]
   Google Scholar
• Barnes , G. , Levi , I. ( 2003 ). Ranks of semigroups generated by order-preserving transformations with a fixed partition type . Comm. Algebra 31 : 1753 – 1763 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Catarino , P. M. , Higgins , P. M. ( 1999 ). The monoid of orientation-preserving mappings on a chain . Semigroup Forum 58 : 190 – 206 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Erdos , J. A. ( 1967 ). On products of idempotent matrices . Glasgow Math. J. 8 : 118 – 122 . [CSA]
   Web of Science ®Google Scholar
• Gomes , G. M. S. , Howie , J. M. ( 1987 ). On the ranks of certain finite semigroups of transformations . Math. Proc. Cambridge Philos. Soc. 101 : 395 – 403 . [CSA]
   Web of Science ®Google Scholar
• Howie , J. M. ( 1966 ). The subsemigroup generated by the idempotents of a full transformation semigroup . J. London Math. Soc. 41 : 707 – 716 . [CSA]
   Web of Science ®Google Scholar
• Howie , J. M. ( 1971 ). Products of idempotents in certain semigroups of transformations . Proc. Edinburgh Math. Soc. 17 ( 2 ): 223 – 236 . [CSA]
   Web of Science ®Google Scholar
• Howie , J. M. ( 1995 ). Fundamentals of Semigroup Theory . London Mathematical Society Monographs. New Series, 12. New York : Oxford Science Publications, The Clarendon Press, Oxford University Press .
   Google Scholar
• Howie , J. M. , McFadden , R. B. ( 1990 ). Idempotent rank in finite full transformation semigroups . Proc. Royal Soc. Edinburgh Sect. A 114 : 161 – 167 . [CSA]
   Web of Science ®Google Scholar
• Levi , I. , McFadden , R. B. ( 1994 ). S n -normal semigroups . Proc. Edinburgh Math. Soc. 37 : 471 – 476 . [CSA]
   Web of Science ®Google Scholar
• Levi , I. , Seif , S. ( 2002 ). Combinatorial techniques for determining rank and idempotent rank of certain finite semigroups . Proc. Edinburgh Math. Soc. 45 ( 2 ): 617 – 630 . [CSA] [CROSSREF]
   Google Scholar
• Levi , I. , Seif , S. ( 2003 ). Counting techniques to label constant weight gray codes with links to minimal generating sets of semigroups . J. Algebra 266 : 220 – 238 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Ruškuc , N. ( 1994 ). On the rank of completely 0-simple semigroups . Math. Proc. Cambridge Philos. Soc. 116 : 325 – 338 . [CSA]
   Web of Science ®Google Scholar
• Communicated by P. Higgins.
   Google Scholar