fair偏序半群的Morita等价
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摘要
设S是满足WRDP的右fair偏序半群且U(S)具有公共弱右局部单位.本文首先介绍了fair偏序半群的一些基本概念和结论,然后给出了这类半群的U(S)的性质,并证明了两半群的酉右S-偏序范畴等价当且仅当两半群闭的右S-偏序范畴等价.最后给出了这类半群Morita等价的等价刻画.
Let S be a fair semigroup whose unitary part has common weak right local units. First,we give some basic notions and results on fair posemigroups which is used in this paper. Then we give some properties of U( S) and prove that Pos-US is equivalent to Pos-UT if and only if Pos-FS is equivalent to Pos-FT.Moreover,we obtain equivalent characterizations of Morita equivalence of these semigroups.
Let S be a fair semigroup whose unitary part has common weak right local units. First,we give some basic notions and results on fair posemigroups which is used in this paper. Then we give some properties of U( S) and prove that Pos-US is equivalent to Pos-UT if and only if Pos-FS is equivalent to Pos-FT.Moreover,we obtain equivalent characterizations of Morita equivalence of these semigroups.
引文
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[12]谢祥云.序半群引论[M].北京:科学出版社,2001.
[13] Tart L. On Morita equivalence of partially ordered semigroups with local units[J]. Acta Comment Univ Tartu Math,2011,15(15):15-33.
[14] Shi X,Liu Z,Wang F,et al.Indecomposable,projective and flat S-posets[J]. Communications in Algebra,2005,33(1):235-251.
[2] Knauer U. Projectivity of acts and Morita equivalence of monoids[J]. Semigroup Forum,1972,3(1):359-370.
[3] Talwar S. Morita equivalence for semigroups[J]. J Aust Math Soc,1995,59(1):81-111.
[4] Lawson M V. Morita equivalence of semigroups with local units[J]. J Pure Appl Algebra,2011,215(4):455-470.
[5] Laan V,Márki L. Fair semigroups and Morita equivalence[J]. Semigroup Forum,2016,92(3):633-644.
[6] Laan V. Morita theorems for partially ordered monoids[J]. Proc Est Acad Sci,2011,60(4):221-237.
[7] Tart L. Strong Morita equivalence for ordered semigroups with local units[J].Periodica Mathematica Hungarica,2012,65(1):29-43.
[8] Howie J M. Fundamentals of Semigroup Theory[M]. New York:Oxford University,1995.
[9] Tart L. Morita invariants for partially ordered semigroups with local units[J]. Proc Est Acad Sci,2012,61(1):38-47.
[10] Jenca G,PulmannováS. Quotients of partial abelian monoids and the Riesz decomposition property[J]. Algebra Universalis,2002,47(4):443-477.
[11] Xie X.On Regular,Strongly regular congruences on ordered semigroups[J]. Semigroup Forum,2000,61(2):159-178.
[12]谢祥云.序半群引论[M].北京:科学出版社,2001.
[13] Tart L. On Morita equivalence of partially ordered semigroups with local units[J]. Acta Comment Univ Tartu Math,2011,15(15):15-33.
[14] Shi X,Liu Z,Wang F,et al.Indecomposable,projective and flat S-posets[J]. Communications in Algebra,2005,33(1):235-251.