On the semigroup of order-decreasing partial isometries of a finite chain

2011/01/13 by R. Kehinde, Rotimi Kehinde, Kehinde, R. +5
Computer Science · Mathematics · #20M20 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20M20 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1101.2558

11 pages

arxiv created 2011/01/13 · openalex publication_date 2011/01/13 · arxiv updated 2011/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \cal I_n be the symmetric inverse semigroup on X_n = \1, 2,..., n\ and let \cal DDP_n and \cal ODDP_n be its subsemigroups of order-decreasing partial isometries and of order-preserving order-decreasing partial isometries of X_n, respectively. In this paper we investigate the cycle structure of order-decreasing partial isometry and characterize the Green's relations on \cal DDP_n and \cal ODDP_n. We show that \cal ODDP_n is a 0-E-unitary ample semigroup. We also investigate the cardinalities of some equivalences on \cal DDP_n and \cal ODDP_n which lead naturally to obtaining the order of the semigroups.

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