Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PRIME RADICALS IN UP-MONOID RINGS

  • Cheon, Jeoung-Soo (Department of Mathematics Pusan National University) ;
  • Kim, Jin-A (Department of Mathematics Pusan National University)
  • Received : 2010.12.24
  • Published : 2012.05.31
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Abstract

We first show that the semiprimeness, primeness, and reducedness can go up to up-monoid rings. By these results we can compute the lower nilradicals of up-monoid rings, from which the well-known fact of Amitsur and McCoy for the polynomial rings can be extended to up-monoid rings.

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References

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Cited by

  1. Properties of Different Prime Radicals of Rings and Modules vol.43, pp.3, 2015, https://doi.org/10.1080/00927872.2013.857237
  2. Nilradicals of the unique product monoid rings vol.16, pp.07, 2017, https://doi.org/10.1142/S021949881750133X