On Pierce Stalks of Semirings
详细信息    查看全文
  • 作者:R. V. Markov ; V. V. Chermnykh
  • 刊名:Journal of Mathematical Sciences
  • 出版年:2016
  • 出版时间:February 2016
  • 年:2016
  • 卷:213
  • 期:2
  • 页码:243-253
  • 全文大小:181 KB
  • 参考文献:1.G. Bredon, Sheaf Theory, McGraw-Hill, New York (1967).MATH
    2.W. D. Burgess and W. Stephenson, “Pierce sheaves of non-commutative rings,” Commun. Algebra, 39, 512–526 (1976).CrossRef MathSciNet
    3.W. D. Burgess and W. Stephenson, “An analogue of the Pierce sheaf for non-commutative rings,” Commun. Algebra, 6, No. 9, 863–886 (1978).CrossRef MathSciNet MATH
    4.W. D. Burgess and W. Stephenson, “Rings all of whose Pierce stalks are local,” Can. Math. Bull., 22, No. 2, 159–164 (1979).CrossRef MathSciNet MATH
    5.A. B. Carson, “Representation of regular rinds of finite index,” J. Algebra, 39, No. 2, 512–526 (1976).CrossRef MathSciNet MATH
    6.V. V. Chermnykh, “Sheaf representations of semirings,” Usp. Mat. Nauk, 48, No. 5, 185–186 (1993).MathSciNet MATH
    7.V. V. Chermnykh, “Functional representations of semirings,” J. Math. Sci., 187, No. 2, 187–267 (2012).CrossRef MathSciNet MATH
    8.V. V. Chermnykh and R. V. Markov, “Pierce chains of semirings,” Vestn. Syktyvkar. Univ., Ser. 1, 16, 88–103 (2012).
    9.V. V. Chermnykh, E. M. Vechtomov, and A. V. Mikhalev, “Abelian regular positive semirings,” Tr. Semin. Petrovskogo, 20, 282–309 (1997).
    10.R. Cignoli, “The lattice of global sections of sheaves of chains over Boolean spaces,” Algebra Universalis, 8, No. 3, 357–373 (1978).CrossRef MathSciNet MATH
    11.S. D. Comer, “Representation by algebras of sections over Boolean spaces,” Pacific. Math., 38, 29–38 (1971).CrossRef MathSciNet MATH
    12.W. H. Cornish, “0-ideals, congruences and sheaf representations of distributive lattices,” Rev. Roum. Math. Pures Appl., 22, No. 8, 200–215 (1977).MathSciNet
    13.J. Dauns and K. H. Hofmann, “The representation of biregular rings by sheaves,” Math. Z., 91, No. 2, 103–123 (1966).CrossRef MathSciNet MATH
    14.G. Georgescu, “Pierce representations of distributive lattices,” Kobe J. Math., 10, No. 1, 1–11 (1993).MathSciNet MATH
    15.K. Keimel, “The representation of lattice ordered groups and rings by sections in sheaves,” in: Lectures on the Applications of Sheaves to Ring Theory, Lect. Notes Math., Vol. 248, Springer, Berlin (1971), pp. 2–96.
    16.J. Lambek, Lectures on Rings and Modules, Waltham, Massachusets (1966)
    17.R. S. Pierce, “Modules over commutative regular rings,” Mem. Amer. Math. Soc., 70, 1–112 (1976).
    18.G. Szeto, “The sheaf representation of near-rings and its applications,” Commun. Algebra, 5, No. 7, 773–782 (1975).CrossRef MathSciNet
    19.A. A. Tuganbaev, Ring Theory. Arithmetical Modules and Rings [in Russian], MCNMO, Moscow (2009).
    20.D. V. Tyukavkin, Pierce Sheaves for Rings with Involution [in Russian], Deposited at VINITI No. 3446-82 (1982).
  • 作者单位:R. V. Markov (1)
    V. V. Chermnykh (1)

    1. Vyatka State University of Humanities, Kirov, Russia
  • 刊物类别:Mathematics and Statistics
  • 刊物主题:Mathematics
    Mathematics
    Russian Library of Science
  • 出版者:Springer New York
  • ISSN:1573-8795
文摘
In this paper, we investigate Pierce stalks of semirings and properties of semirings lifted from properties of the stalks. We distinguish classes of semirings that admit characterization by properties of their Pierce sheaves. Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 2, pp. 171–186, 2014.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700