关于交换的弱归~＊-半环的研究

On commutative weak inductive ＊-semirings

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摘要研究了交换的弱归纳*-半环S上的二阶方阵半环S2×2.给出S2×2仍为弱归纳的一个充分条件.即若S2×2是λ-半环,则S2×2是弱归*-半环.应用这一结果可以证明S上的二元仿射映射存在最小的联立不动点,部分回答了相关文献中的公开问题. The semiring S2×2 of 2 × 2 matrices over a commutative weak inductive ＊-semiring S is studied.It is shown that if 2 × 2 is a λ-semiring then it is a weak inductive ＊-semiring again.Then the least simultaneous fixed points of two binary affne maps over S are given. 更多还原

作者沈晓芹田径丰丕虎

机构地区西安理工大学理学院西北大学数学系

出处《纯粹数学与应用数学》 CSCD 2012年第4期540-545,共6页 Pure and Applied Mathematics

基金国家自然科学基金(11101330) 陕西省自然科学基金青年基金(2011JQ1007)

关键词 λ-半环＊-半环矩阵半环最小联立不动点 λ-semiring；＊-semiring； matrices semirings； least simultaneous fixed points

分类号 O153.3 [理学—基础数学]

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参考文献8

1冯锋,柳晓燕.弱归纳*-半环上仿射映射的联立不动点(英文)[J].数学进展,2008,37(3):283-290. 被引量：2
2Tarski A. A lattice-theoretical fixpoint theorem and its applications [J]. Pacific Journal of Mathematics, 1955,5:285-309.
3Davis A, A characterization of complete lattices[J]. Pacific Journal of Mathematics, 1955,5:311-319.
4Abian A, Brown A. A theorem on partially ordered sets with applications to fixed point theorems [J]. Canadian J. of Math., 1961,13:173-174.
5Golan J. The Theory of Semirings, with Applications in Mathematics and Theoretical Computer Science[M]. Harlow: Longman Scientific and Technical, 1992.
6Esik Z, Kuich W. Inductive *-semirings [J]. Theoretical Computer Science, 2004,324:3-33.
7Conway J. Regular Algebra and Finite Machines[M]. London: Chapman and Hall, 1971.
8Feng F, Zhao X,Jun Y. B semirings and semirings [J]. Theoretical Computer Science, 2005,347:423-431.

二级参考文献12

1[1]Bloom,S.L.,Esik Z,Matrix and matrical iteration theories,part I,J.Comput.System Sci.,1993,46:381-408.
2[2]Bloom,S.L.,Esik Z,Iteration Theories:the Equational Logic of Iterative Processes,EATCS Monographs on Theoretical Computer Science,Berlin:Springer,1993.
3[3]Bloom,S.L.,Esik Z,The equational logic of fixed points,Theater.Comput.Sci.,1997,179:1-60.
4[4]Conway,J.H.,Regular Algebra and Finite Machines,London:Chapman and Hall,1971.
5[5]Davey,B.A.,Priestly,H.A.,Introduction to Lattices and Order,Cambridge:Cambridge University Press,1990.
6[6]Esik,Z.,Kuich,W.,Inductive *-semirings,Theoret.Comput.Sci.,2004,324:3-33.
7[7]Feng F.,Zhao X.Z.,Jun Y.B.,*-μ-semirings and *-λ-semirings,Theoret.Comput.Sci.,2005,347:423-431.
8[8]Golan,J.S.,Semirings and Affine Equations over Them:Theory and Applications,Dordrecht:Kluwer,2003.
9[9]Goldstern,M.,Vervollstandigung yon Halbringen,Diploma Thesis,Technical University of Vienna,1985.
10[10]Kozen,D.,On Kleene algebras and closed semirings,Proc.MFCS'90,Lecture Notes in Computer Science,vol.452,Rovan (Ed.),Berlin:Springer,1990,26-47.

共引文献1

1柳晓燕,冯锋.Kleene代数及相关半模结构[J].数学的实践与认识,2010,40(11):198-205.

1庄金洪,谭宜家.关于矩阵半环的导子[J].福州大学学报（自然科学版）,2008,36(5):634-638.
2孟丽娜,郑宝东,田国华.非负交换整半环上矩阵的积和式保持问题[J].哈尔滨理工大学学报,2010,15(1):70-72.
3黄惠玲.交换半环上上三角矩阵半环的自同构[J].延安大学学报（自然科学版）,2014,33(3):17-20.
4雷晓敏,元文娥,李婷婷.ω-Conway半环与ω-归纳~＊-半环[J].纺织高校基础科学学报,2011,24(2):256-260.
5毛福海,冯立.关于一类*-λ-半环[J].延安大学学报（自然科学版）,2009,28(2):7-10. 被引量：1
6龙伦海.准仿射映射及其生成的分形[J].海南大学学报（自然科学版）,2003,21(3):203-206. 被引量：1
7龙伦海,向炎春.由准仿射映射生成的分形的维数[J].海南大学学报（自然科学版）,2009,27(2):119-122.
8石定琴.矩阵半环D_3(R,I)[J].江西科学,2012,30(3):288-291.
9段俊生,陈占华.有零分配格上矩阵半环的理想格[J].内蒙古工业大学学报（自然科学版）,2001,20(4):288-289.
10王力,冯立,王青茹.UF-归纳^＊-半环和UF-弱归纳^＊-半环[J].纺织高校基础科学学报,2010,23(2):180-184.

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关于交换的弱归~＊-半环的研究

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