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Axiomatic definition of a quotient ring

  • V. P. Elizarov
Article
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Abstract

The quotient ring QΦ(R) of the ring R with respect to a strong filter Φ of right ideals of R is axiomatically defined as a maximal strong Φ-essential extension of R. The ring QΦ(R) is constructively obtained in the form of lim Homr (I, R), where I ∈ Φ.

Keywords

Quotient Ring Axiomatic Definition Strong Filter 
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Literature cited

  1. 1.
    V. P. Elizarov, “Strong pretorsions and strong filters, modules and quotient rings,” Sibirsk. Matem. Zh.,14, No. 3, 549–559 (1973).Google Scholar
  2. 2.
    B. Stenström, “Rings and modules of quotients,” Lecture Notes in Math., 237 (1971).Google Scholar
  3. 3.
    J. Lambek, “Torsion theories; additive semantics and rings of quotients,” Lecture Notes in Math., 177 (1971).Google Scholar
  4. 4.
    D. F. Sanderson, “A generalization of divisibility and injectivity in modules,” Canad. Math. Bull.,8, 505–513 (1965).Google Scholar
  5. 5.
    Y. Utumi, “On quotient rings,” Osaka Math. J.,8, 1–18 (1956).Google Scholar
  6. 6.
    V. P. Elizarov, “On the general theory of quotient rings,” Sibirsk. Matem. Zh.,11, No. 3, 526–546 (1970).Google Scholar

Copyright information

© Consultants Bureau 1974

Authors and Affiliations

  • V. P. Elizarov

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