On the ranks of certain ideals of monotone contractions

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BUGAY L.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.49, sa.6, ss.1988-1996, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 6
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15672/hujms.604715
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1988-1996
  • Anahtar Kelimeler: isotone/antitone/monotone transformation, contraction, rank
  • Çukurova Üniversitesi Adresli: Evet

Özet

Let T-n be the (full) transformation semigroup, and let OCTn and ORCTn be its subsemigroups of isotone contractions and of monotone contractions on a finite chain X-n = {1, ..., n} under its natural order, respectively. In this study, we obtain the ranks of the ideals OCTn,r = {alpha is an element of OCTn : vertical bar im (alpha)vertical bar <= r} and ORCTn,r =vertical bar im (alpha)vertical bar <= r} for 1 <= r <= n - 1.