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ArticleOriginal scientific text

Title

Localization in semicommutative (m,n)-rings

Authors 1, 2

Affiliations

  1. Institut Girard Desargues, bat. 101, Université Lyon 1, 43 bd du 11 Novembre 1918, F-69622 Villeurbanne, France
  2. North University of Baia Mare, Victoriei 76, 4800 Baia Mare, Romania

Abstract

We give a construction for (m,n)-rings of quotients of a semicommutative (m,n)-ring, which generalizes the ones given by Crombez and Timm and by Paunić for the commutative case. We also study various constructions involving reduced rings and rings of quotients and give some functorial interpretations.

Keywords

ENG
(m,n)-rings, semicommutative (m,n)-rings, (m,n)-rings of quotients, (m,n)-division rings, (m,n)-semidomains, n-groups, n-semigroups

Bibliography

  1. G. Crombez, On (n,m)-rings, Abh. Math. Sem. Univ. Hamburg 37 (1972), 180-199.
  2. G. Crombez and J. Timm, On (n,m)-quotient rings, Abh. Math. Sem. Univ. Hamburg 37 (1972), 200-203.
  3. W. Dörnte, Untersuchungen über einen verallgemeinerten Gruppenbegriff, Math. Z. 29 (1928), 1-19.
  4. W.A. Dudek, On the divisibility theory in (m, n)-rings, Demonstratio Math. 14 (1981), 19-32.
  5. W.A. Dudek and J. Michalski, On a generalization of Hosszú theorem, Demonstratio Math. 15 (1982), 783-805.
  6. W.A. Dudek and J. Michalski, On retracts of polyadic groups, Demonstratio Math. 17 (1984), 281-301.
  7. K. Głazek and B. Gleichgewicht, Abelian n-groups, Coll. Math. Soc. János Bolyai Universal Algebra, Esztergom (Hungary) 29 (1977), 321-329.
  8. L. Iancu, A note on the reduction of n-semigroups of fractions, Bul. St. Univ. Baia Mare, ser. B, Mat.-Inf. 13 (1997), 5-10.
  9. J. Michalski, On some functors from the category of n-groups, Bull. Acad. Pol. Sci. Sér. Sci. Math. 27 (1979), 437-441.
  10. Dj. Paunić, Localization in (m,n)-rings, 'Proceedings of the Conference Algebra and Logic, Zagreb 1984', Univ. Novi Sad 1985, 123-133.
  11. M.S. Pop, On the reduction and extension of (m,n)-rings, Bul. St. Univ. Baia Mare, ser. B, Mat.-Inf. 9 (1993), 81-90.
  12. M.S. Pop and M. Campian, n-Semigroups of fractions, Mathematica 38 (61) (1996), 63-68.
  13. E.L. Post, Polyadic groups, Trans. Amer. Math. Soc. 48 (1940), 208-350.
  14. I. Purdea, Les anneaux de type (m, n), Studia Univ. Babes-Bolyai Cluj 20 (1975), 3-10.
  15. J. Timm, Kommutative n-gruppen, Dissertation Hamburg 1967.
Discussiones Mathematicae - General Algebra and Applications
2000/20/2
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Pages:
233-253
Main language of publication
English
Received
1999-01-20
Accepted
2000-09-20
Published
2000

DOI: 10.7151/dmgaa.1020

Exact and natural sciences