Abstract
We prove a theorem on the commutativity of the PI ring and use it to generalize a famous theorem of Herstein.
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C. L. Fu, Y. C. Guo, Commutativity conditions for semiprime rings, Acta Mathematica Sinica, 1995, 38(2):242–247
I. N. Herstein, A condition for commutativity of rings, Canad. Math., 1957, 9:583–586
T. P. Kezlan, A note on commutativity of semiprime PI-ring, Math. Japan, 1982, 27:267–268
T. P. Kezlan, A commutativity theorem involving certain polynomial constraints, Math. Japan, 1991, 36(4):785–789
N. Jacobson, Structure of rings, Amer. Math. Soc., Colloq., Publ., 1964, 37
H. A. S. Abujabal, M. S. Khan, A commutativity result for rings, Bull. Inst. Math. Sinica, (18):333–337
M. A. Quadri, On commutativity of associative rings, Bull. Austral Math. Soc., 1998, 38(2):267–271
M. Ashraf, M. A. Ali Asma Quadri. On commutativity of one sided s-unital rings, Rad. Math., 1990, 6(1):111–117
Tsunckazu Nishinaka, A commutativity theorem for rings, Rad. Math., 1990, 6(2):357–359
H. A. S. Abujabal, M. S. Khan, On commutativity theorems for rings, Internat J. Math. Sci., 1990, 13(1):87–92
H. A. S. Abujabal, Two commutativity results for ring, Math. Japan, 1990, 38(2):279–299
M. A. Quadri, M. A. Khan, Math. Japan, 1990, 33(2):275–279
T. P. Kezlan, On identities which are equivalent with commutativity, Math. Japan, 1984, 29(1):135–139
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Fu, C.L., Yang, X.S. Two Theorems on the Commutativity of Arbitrary Rings. Acta Math Sinica 17, 133–140 (2001). https://doi.org/10.1007/s101149900018
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DOI: https://doi.org/10.1007/s101149900018