http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET
Honyam, Preeyanuch,Sanwong, Jintana Korean Mathematical Society 2011 대한수학회지 Vol.48 No.2
Let T(X) denote the semigroup (under composition) of transformations from X into itself. For a fixed nonempty subset Y of X, let S(X, Y) = {${\alpha}\;{\in}\;T(X)\;:\;Y\;{\alpha}\;{\subseteq}\;Y$}. Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) is isomorphic to T(Z) for some set Z and prove that every semigroup A can be embedded in S($A^1$, A). Then we describe Green's relations for S(X, Y) and apply these results to obtain its group H-classes and ideals.
INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS
Singha, Boorapa,Sanwong, Jintana,Sullivan, Robert Patrick Korean Mathematical Society 2012 대한수학회보 Vol.49 No.1
In 2003, Marques-Smith and Sullivan described the join ${\Omega}$ of the 'natural order' $\leq$ 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 $\leq$ 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 $\leq$ 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.
Ideals of the Multiplicative Semigroups ℤ<sub>n</sub> and their Products
Puninagool, Wattapong,Sanwong, Jintana Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.1
The multiplicative semigroups $\mathbb{Z}_n$ have been widely studied. But, the ideals of $\mathbb{Z}_n$ seem to be unknown. In this paper, we provide a complete descriptions of ideals of the semigroups $\mathbb{Z}_n$ and their product semigroups ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$. We also study the numbers of ideals in such semigroups.
SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET
Preeyanuch Honyam,Jintana Sanwong 대한수학회 2011 대한수학회지 Vol.48 No.2
Let T(X) denote the semigroup (under composition) of trans-formations from X into itself. For a fixed nonempty subset Y of X, let S(X, Y) = <수식>Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X,Y)is isomorphic to T(Z) for some set Z and prove that every semigroup A can be embedded in S(A^1,A). Then we describe Green's relations for S(X,Y) and apply these results to obtain its group H-classes and ideals.
INJECTIVE PARTIAL TRANSFORMATIONS WITH INFINITE DEFECTS
Boorapa Singha,Jintana Sanwong,Robert Patrick Sullivan 대한수학회 2012 대한수학회보 Vol.49 No.1
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.