# 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

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topLăcrimioara 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

top- [1] G. Crombez, On (n,m)-rings, Abh. Math. Sem. Univ. Hamburg 37 (1972), 180-199. Zbl0247.08001
- [2] G. Crombez and J. Timm, On (n,m)-quotient rings, Abh. Math. Sem. Univ. Hamburg 37 (1972), 200-203. Zbl0247.08002
- [3] W. Dörnte, Untersuchungen über einen verallgemeinerten Gruppenbegriff, Math. Z. 29 (1928), 1-19. Zbl54.0152.01
- [4] W.A. Dudek, On the divisibility theory in (m, n)-rings, Demonstratio Math. 14 (1981), 19-32. Zbl0471.16027
- [5] W.A. Dudek and J. Michalski, On a generalization of Hosszú theorem, Demonstratio Math. 15 (1982), 783-805. Zbl0523.20045
- [6] W.A. Dudek and J. Michalski, On retracts of polyadic groups, Demonstratio Math. 17 (1984), 281-301. Zbl0573.20067
- [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] 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] 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] 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. Zbl0798.16040
- [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. Zbl66.0099.01
- [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.

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