保等价部分变换半群的变种半群上的正则元The regular element for variant semigroup of partial transformation semigroup preserving an equivalence relation
秦美青;许新斋;
摘要(Abstract)：
在现有的保等价部分变换半群的基础上,引入了一个新的运算,得出保等价部分变换半群的变种半群的概念,利用格林关系及幂等元的正则性,讨论了这类半群中元素的正则性,给出了保等价部分变换半群的变种半群中一个元是正则元的充要条件
关键词(KeyWords)： 变换半群;保等价部分变换半群的变种半群;正则元
基金项目(Foundation): 山东省教育厅科技计划项目(J06P18)
作者(Authors): 秦美青;许新斋;
参考文献(References)：
- [1]Pei Huisheng.Green’s relations for the variants of transformation semigroups preserving an equivalencerelation[J].Communications in Algebra,2007,35:1971-1986.
- [2]Pei Huisheng.Semigroups of partial transformations preserving an equivalence relation[J].数学进展,2009,38(1):103-118.
- [3]Pei Huisheng.Regularlty and Green’s relations for semigroups of transformations that preserve an equiva-lence[J].Communications in Algebra,2005,33:109-108.
- [4]裴惠生,孙垒.一类变换半群的正则元和Green关系[J].数学研究与评论,2007,27(3):591-600.
- [5]许新斋,孟玲.奇异保序变换半群的极大正则子半群[J].纯粹数学与应用数学,2009,25(3):508-511.
- [6]Magill Jr K D,Subbian S.Green’s relations for regular elements of Sandwich semigroup,(I)general results[J].London Math.Soc.,1975,3(31):194-210.
- [7]Magill Jr K D,Subbian S.Green’s relations for regular elements of Sandwich semigroup,(II)semigroups ofcontinuous function[J].Austral.Math.Soc.,1978,25(A):45-65.
- [8]You T.Maximal regular subsemigroups of certain semigroups of transformations[J].Semigroup Forum,2002,64:391-396.
- [9]陈迪三.强P-正则半群上的最小正则-半群同余[J].纯粹数学与应用数学,2009,25(1):142-144.
- [10]Howie J M.Fundamentals of Semigroup Theory[M].New York:Oxford University Press,1995.