On semiprime P. I. rings

Martindale, Wallace S.

doi:10.1090/S0002-9939-1973-0318215-3

On semiprime P. I. rings
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by Wallace S. Martindale

Proc. Amer. Math. Soc. 40 (1973), 365-369

DOI: https://doi.org/10.1090/S0002-9939-1973-0318215-3

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Abstract:

The main results proved in this paper are that if $R$ is a semiprime ring satisfying a polynomial identity then (1) the maximal right quotient ring of $R$ is also P.I. and (2) every essential one-sided ideal of $R$ contains an essential two-sided ideal of $R$.

References

Joe W. Fisher, Structure of semiprime P.I. rings, Proc. Amer. Math. Soc. 39 (1973), 465–467. MR 320049, DOI 10.1090/S0002-9939-1973-0320049-0
Edward Formanek, Central polynomials for matrix rings, J. Algebra 23 (1972), 129–132. MR 302689, DOI 10.1016/0021-8693(72)90050-6
I. N. Herstein and Lance W. Small, Regular elements in $\textrm {P}.\textrm {I}.$-rings, Pacific J. Math. 36 (1971), 327–330. MR 281751, DOI 10.2140/pjm.1971.36.327
Louis Rowen, Some results on the center of a ring with polynomial identity, Bull. Amer. Math. Soc. 79 (1973), 219–223. MR 309996, DOI 10.1090/S0002-9904-1973-13162-3
Y. Utumi, On rings of which any one-sided quotient rings are two-sided, Proc. Amer. Math. Soc. 14 (1963), 141–147. MR 142568, DOI 10.1090/S0002-9939-1963-0142568-6