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PRIME RADICALS IN UP-MONOID RINGS

  • Received : 2010.12.24
  • Published : 2012.05.31

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.

Keywords

up-monoid ring;lower nilradical;upper nilradical;(semi)prime ring;reduced ring

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