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The preservation of the semiprime Goldie property by strong semilattice sums

Author: Yue-chan P. Ho
Journal: Proc. Amer. Math. Soc. 114 (1992), 613-616
MSC: Primary 16P60; Secondary 16W50, 20M25
MathSciNet review: 1074752
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Abstract: Let $ R$ be a strong semilattice sum of rings $ {R_\alpha }(\alpha \in P)$ where $ P$ is an m.u.-semilattice. When $ P$ is infinite, $ R$ is not a right Goldie ring; and when $ P$ is finite, $ R$ is semiprime right Goldie iff each $ {R_\alpha }$ is semiprime right Goldie.

References [Enhancements On Off] (What's this?)

  • [1] M. L. Teply, E. G. Turman, and A. Quesada, On semisimple semigroup rings, Proc. Amer. Math. Soc. 79 (1980), 157-163. MR 565329 (81f:20094)
  • [2] H. L. Chick and B. J. Gardner, The preservation of some ring properties by semilattice sums, Comm. Algebra 15 (1987), 1017-1038. MR 879351 (88a:16015)
  • [3] E. G. Turman, Supplementary semilattice sums of rings, Ph.D. dissertation, Univ. of Florida, 1980.
  • [4] I. N. Herstein, Noncommutative rings, Math. Assoc. Amer., distributed by J. Wiley, 1968. MR 0227205 (37:2790)
  • [5] T. W. Hungerford, Algebra, Springer-Verlag, New York, 1974. MR 600654 (82a:00006)
  • [6] B. Stenström, Rings of quotients, Springer-Verlag, New York, 1975. MR 0389953 (52:10782)

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Keywords: Semilattice sum, semiprime Goldie
Article copyright: © Copyright 1992 American Mathematical Society

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