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In 2003, Marques-Smith and Sullivan described the join ${\Omega}$ of the 'natural order' ≤ and the 'containment order' $\subseteq$ on P(X), the semigroup under composition of all partial transformations of a set X. And, in 2004, Pinto and Sullivan described all automorphisms of PS(q), the partial Baer-Levi semigroup consisting of all injective ${\alpha}{\in}P(X)$ such that ${\mid}X{\backslash}X{\alpha}\mid=q$, where $N_0{\leq}q{\leq}{\mid}X{\mid}$. In this paper, we describe the group of automorphisms of R(q), the largest regular subsemigroup of PS(q). In 2010, we studied some properties of ≤ and $\subseteq$ on PS(q). Here, we characterize the meet and join under those orders for elements of R(q) and PS(q). In addition, since ≤ does not equal ${\Omega}$ on I(X), the symmetric inverse semigroup on X, we formulate an algebraic version of ${\Omega}$ on arbitrary inverse semigroups and discuss some of its properties in an algebraic setting.
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참고문헌 (14)
참고문헌 신청
A. H. Clifford / 1967 / The Algebraic Theory of Semigroups, Mathematical Surveys, No. 7, vol 1 and 2 / American Mathematical Society
B. Singha / 2010 / Partial orders on partial Baer-Levi semi- groups / Bull. Aust. Math. Soc 81 (2) : 195 ~ 207
F. A. Pinto / 2004 / Baer-Levi semigroups of partial transformations / Bull. Aust. Math. Soc 69 (1) : 87 ~ 106
G. Kowol / 1986 / Naturally ordered transformation semigroups / Monatsh. Math 102 (2) : 115 ~ 138
H. Mitsch / 1986 / A natural partial order for semigroups / Proc. Amer. Math. Soc 97 (3) : 384 ~ 388
B. Singha / 2010 / Partial orders on partial Baer-Levi semi- groups / Bull. Aust. Math. Soc 81 (2) : 195 ~ 207
F. A. Pinto / 2004 / Baer-Levi semigroups of partial transformations / Bull. Aust. Math. Soc 69 (1) : 87 ~ 106
G. Kowol / 1986 / Naturally ordered transformation semigroups / Monatsh. Math 102 (2) : 115 ~ 138
H. Mitsch / 1986 / A natural partial order for semigroups / Proc. Amer. Math. Soc 97 (3) : 384 ~ 388
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