幂半群上Green关系的若干性质
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摘要
本文主要研究了半群S的幂半群P(S)上Green关系的若干性质.证明了对任意的a∈S,a在S和P(S)中的L类,R类,H类之间的关系.同时,对完全正则半群S,证明了P(S)中的两个元素A,B在同一R类(或同一L类,H类)时,Id A=Id B.
The paper gives a semigroup S,some properties of Green's relation on the power semigroup P( S)of S are studied. The relations of the L-class La( S)( the R-class Ra( S),the H-class Ha( S),respectively) and the L-class La( P( S))( the R-class Ra( P( S)),the H-class Ha( P( S)),respectively) are discussed. Also,it is proved that for any A,B ∈ P( S),Id A = Id B if either ALP( S)B or ARP( S)B.
The paper gives a semigroup S,some properties of Green's relation on the power semigroup P( S)of S are studied. The relations of the L-class La( S)( the R-class Ra( S),the H-class Ha( S),respectively) and the L-class La( P( S))( the R-class Ra( P( S)),the H-class Ha( P( S)),respectively) are discussed. Also,it is proved that for any A,B ∈ P( S),Id A = Id B if either ALP( S)B or ARP( S)B.
引文
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[10] GAN A P,ZHAO X Z. Global determinism of clifford semigroups[J]. J Aust Math Soc,2014,97:63-77.
[2] PAZY A. Semigroups of linear operator and applications to partial differential equations[M]. New York:SpringerVerlag,1983.
[3] HOWIE J M. Automata and languages[M]. Oxford:Clarendon Press,1991.
[4] HOWIE J M. Fundamentals of semigroup theory[M]. Oxford:Clarendon Press,1995.
[5] TAMURA T. Unsolved problems on semigroups[R]. Kyoto:Seminar Reports of Math Sci,1967.
[6] TAMURA T,SHAFER J. Power semigroups[J]. Math Japon,1967,12,25-32.
[7] TAMURA T,SHAFER J. Power semigroups II[J]. Notices,1968,15:395.
[8] ALMEIDA J. Power semigroups:results and problems[J]. Algebraic Engineering,1999,399-415.
[9] GOULD M,ISKRA J A. Globally determined classes of semigroups[J]. Semigroup Forum,1984,28:1-11.
[10] GAN A P,ZHAO X Z. Global determinism of clifford semigroups[J]. J Aust Math Soc,2014,97:63-77.