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COMMUTATIVITY OF RINGS WITH CONSTRAINTS ON COMMUTATORS

Journal Name:

  • İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi

Publication Year:

  • 2000

Key Words:

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper, we study the commutativity of a ring R satisfying the polynomial identity xt[xn,y]yr = ±[x,ym]ys (resp. a;*[a;n,y]yr = ±ys[x, ym]), for all x,y € R, where m,n,r,s and t are some non-negative integers such that m > 0, n > 0, and m = nifn + i^l and m + + The main results of the present paper assert that a. semiprime ring R is commutative if (m,n,r,s,t) ^ (0,0,0,0,0) and commutativity of an associative ring R follows with property Q(m), for m > 1, n > 1, that is for all x,y G R, m[x,y] = 0 implies [x,y] = 0. It is also shown that the above results are true for s-unital rings. Finally, our results generalize some of the well-known commutativity theorems for rings (see [1, 2, 5, 10, 12, 15]).
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29-45
  • English

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REFERENCES

References: 

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11. KOMATSU, H., A commutativity theorem for rings, Math. J. Okayama Univ. 26 (1984), 109 - 111.
12. PSOMOPOULES, E., Commutativity theorems for rings and groups with constraints on commutators, Internat J. Math, and Math. Sci. 7 (1984), 513 - 517
13. QUADRI, M. A. and KHAN, M. A., A commutativity theorem for left s-unital rings, Bull. Inst. Math. Acad. Sinica 15 (1987), 323 -327.
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14. STREB, W., Zur struktur nichtkommutativer ringe, Math. J. Okayama Univ. 31 (1989), 135 - 140.
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an
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