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Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2012; 49(3): 511-515

Printed May 1, 2012

https://doi.org/10.4134/BKMS.2012.49.3.511

Copyright © The Korean Mathematical Society.

Prime radicals in up-monoid rings

Jeoung Soo Cheon and Jin-A Kim

Pusan National University, Pusan National University

Abstract

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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

MSC numbers: Primary 16N40, 16N60

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