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In this note we consider the monoid $\PODI_n$ of all monotone partial permutations on $\{1,\ldots,n\}$ and its submonoids $\DP_n$, $\POI_n$ and $\ODP_n$ of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids $\POI_n$ and $\ODP_n$ are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that $\PODI_n$ is a quotient of a semidirect product of $\POI_n$ and the group $\mathcal{C}_2$ of order two and, analogously, $\DP_n$ is a quotient of a semidirect product of $\ODP_n$ and $\mathcal{C}_2$.
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참고문헌 (36)
참고문헌 신청
A. Ya. Aızenstat / 1962 / The defining relations of the endomorphism semigroup of a finite linearly ordered set / Sibirsk. Mat. Z 3:161~169
F. Al-Kharousi / 2014 / Combinatorial results for certain semigroups of partial isometries of a finite chain / Australas. J. Combin 58(3):365~375
F. Al-Kharousi / On the semigroup of partial isometries of a finite chain / Communications in Algebra
C. J. Ash / 1987 / Finite semigroups with commuting idempotents / J. Austral. Math. Soc. Ser. A 43(1):81~90
D. F. Cowan / 1995 / Partial cross-sections of symmetric inverse semigroups / Int. J. Algebra Comput 5(3):259~287
F. Al-Kharousi / 2014 / Combinatorial results for certain semigroups of partial isometries of a finite chain / Australas. J. Combin 58(3):365~375
F. Al-Kharousi / On the semigroup of partial isometries of a finite chain / Communications in Algebra
C. J. Ash / 1987 / Finite semigroups with commuting idempotents / J. Austral. Math. Soc. Ser. A 43(1):81~90
D. F. Cowan / 1995 / Partial cross-sections of symmetric inverse semigroups / Int. J. Algebra Comput 5(3):259~287
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