关于反射等价关系的变换半群的注记
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摘要
设TX是非空集合X上全变换半群,E是X上非平凡的等价关系,则T?(X)是TX的子半群.在赋予半群T?(X)自然偏序关系的条件下,本文刻画了它的相容元.
Let TXbe the full transformation semigroup on a nonempty set X and E be a nontrivial equivalence relation on X, then T?(X) is a subsemigroup of TX. In this paper, we describe all the left and right compatible elements in the transformation semigroup T?(X) endowed with the natural partial order.
Let TXbe the full transformation semigroup on a nonempty set X and E be a nontrivial equivalence relation on X, then T?(X) is a subsemigroup of TX. In this paper, we describe all the left and right compatible elements in the transformation semigroup T?(X) endowed with the natural partial order.
引文
[1]Mitsch H.A natural partial order for semigroups[J].Proceedings of the American Mathematical Society,1986,97(3):384-388.
[2]Kowol G,Mitsch H.Naturally ordered transformation semigroups[J].Monatshefte Fur Mathematik,1986,102(2):115-138.
[3]Marques-Smith M Paula O,Sullivan R P.Partial orders on transformation semigroups[J].Monatshefte Fur Mathematik,2003,140(2):103-118.
[4]Sullivan R P.Partial orders on linear transformation semigroups[J].Proceedings of the Royal Society Edinburgh Section A-Mathematics,2005,135(2):413-437.
[5]Sun L,Deng W N,Pei H S.Naturally ordered transformation semigroups preserving an equivalence and a cross-section[J].Algebra Colloquium,2011,18(3):523-532.
[6]Deng L Z,Zeng J W,You T J.Green′s relations and regularity for semigroups of transformations that preserve reverse direction equivalence[J].Semigroup Forum,2011,83(3):489-498.
[7]Sun L,Xin X J.The natural partial order on the semigroup of all transformations of a set that reflect on equivalence relation[J].Bullet of the Australian Mathematical Society,2013,88(3):359-368.
[2]Kowol G,Mitsch H.Naturally ordered transformation semigroups[J].Monatshefte Fur Mathematik,1986,102(2):115-138.
[3]Marques-Smith M Paula O,Sullivan R P.Partial orders on transformation semigroups[J].Monatshefte Fur Mathematik,2003,140(2):103-118.
[4]Sullivan R P.Partial orders on linear transformation semigroups[J].Proceedings of the Royal Society Edinburgh Section A-Mathematics,2005,135(2):413-437.
[5]Sun L,Deng W N,Pei H S.Naturally ordered transformation semigroups preserving an equivalence and a cross-section[J].Algebra Colloquium,2011,18(3):523-532.
[6]Deng L Z,Zeng J W,You T J.Green′s relations and regularity for semigroups of transformations that preserve reverse direction equivalence[J].Semigroup Forum,2011,83(3):489-498.
[7]Sun L,Xin X J.The natural partial order on the semigroup of all transformations of a set that reflect on equivalence relation[J].Bullet of the Australian Mathematical Society,2013,88(3):359-368.