Localization in semicommutative (m,n)-rings

Lăcrimioara Iancu; Maria S. Pop

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 2, page 233-253
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Lăcrimioara Iancu, and Maria S. Pop. "Localization in semicommutative (m,n)-rings." Discussiones Mathematicae - General Algebra and Applications 20.2 (2000): 233-253. <http://eudml.org/doc/287724>.

@article{LăcrimioaraIancu2000,
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.},
author = {Lăcrimioara Iancu, Maria S. Pop},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {(m,n)-rings; semicommutative (m,n)-rings; (m,n)-rings of quotients; (m,n)-division rings; (m,n)-semidomains; n-groups; n-semigroups; -ary group; -ring; -semigroup},
language = {eng},
number = {2},
pages = {233-253},
title = {Localization in semicommutative (m,n)-rings},
url = {http://eudml.org/doc/287724},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Lăcrimioara Iancu
AU - Maria S. Pop
TI - Localization in semicommutative (m,n)-rings
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 2
SP - 233
EP - 253
AB - 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.
LA - eng
KW - (m,n)-rings; semicommutative (m,n)-rings; (m,n)-rings of quotients; (m,n)-division rings; (m,n)-semidomains; n-groups; n-semigroups; -ary group; -ring; -semigroup
UR - http://eudml.org/doc/287724
ER -

References

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  1. [1] G. Crombez, On (n,m)-rings, Abh. Math. Sem. Univ. Hamburg 37 (1972), 180-199. Zbl0247.08001
  2. [2] G. Crombez and J. Timm, On (n,m)-quotient rings, Abh. Math. Sem. Univ. Hamburg 37 (1972), 200-203. Zbl0247.08002
  3. [3] W. Dörnte, Untersuchungen über einen verallgemeinerten Gruppenbegriff, Math. Z. 29 (1928), 1-19. Zbl54.0152.01
  4. [4] W.A. Dudek, On the divisibility theory in (m, n)-rings, Demonstratio Math. 14 (1981), 19-32. Zbl0471.16027
  5. [5] W.A. Dudek and J. Michalski, On a generalization of Hosszú theorem, Demonstratio Math. 15 (1982), 783-805. Zbl0523.20045
  6. [6] W.A. Dudek and J. Michalski, On retracts of polyadic groups, Demonstratio Math. 17 (1984), 281-301. Zbl0573.20067
  7. [7] K. Głazek and B. Gleichgewicht, Abelian n-groups, Coll. Math. Soc. János Bolyai Universal Algebra, Esztergom (Hungary) 29 (1977), 321-329. Zbl0487.20042
  8. [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. Zbl1051.20504
  9. [9] J. Michalski, On some functors from the category of n-groups, Bull. Acad. Pol. Sci. Sér. Sci. Math. 27 (1979), 437-441. Zbl0424.18003
  10. [10] Dj. Paunić, Localization in (m,n)-rings, 'Proceedings of the Conference Algebra and Logic, Zagreb 1984', Univ. Novi Sad 1985, 123-133. 
  11. [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. Zbl0798.16040
  12. [12] M.S. Pop and M. Campian, n-Semigroups of fractions, Mathematica 38 (61) (1996), 63-68. 
  13. [13] E.L. Post, Polyadic groups, Trans. Amer. Math. Soc. 48 (1940), 208-350. Zbl66.0099.01
  14. [14] I. Purdea, Les anneaux de type (m, n), Studia Univ. Babes-Bolyai Cluj 20 (1975), 3-10. 
  15. [15] J. Timm, Kommutative n-gruppen, Dissertation Hamburg 1967. 

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