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PRIME RADICALS IN UP-MONOID RINGS
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 Title & Authors
PRIME RADICALS IN UP-MONOID RINGS
Cheon, Jeoung-Soo; Kim, Jin-A;
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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.
 Keywords
up-monoid ring;lower nilradical;upper nilradical;(semi)prime ring;reduced ring;
 Language
English
 Cited by
1.
Properties of Different Prime Radicals of Rings and Modules, Communications in Algebra, 2015, 43, 3, 971  crossref(new windwow)
2.
Nilradicals of the unique product monoid rings, Journal of Algebra and Its Applications, 2017, 16, 07, 1750133  crossref(new windwow)
 References
1.
V. Camillo, C. Y. Hong, N. K. Kim, Y. Lee, and P. P. Nielsen, Nilpotent ideals in polynomial and power series rings, Proc. Amer. Math. Soc. 138 (2010), no. 5, 1607-1619. crossref(new window)

2.
C. Y. Hong, N. K. Kim, and Y. Lee, Extensions of McCoy's theorem, Glasg. Math. J. 52 (2010), no. 1, 155-159. crossref(new window)

3.
E. Jespersa, J. Krempa, and E. R. Puczylowski, On radicals of graded rings, Comm. Algebra. 10 (1982), 1849-1854. crossref(new window)

4.
T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 1991.

5.
J. Lambek, On the representations of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1971), 359-368. crossref(new window)

6.
J. Okninski, Semigroup Algebras, Marcel Dekker, New York, 1991.

7.
D. S. Passman, The Algebraic Structure of Group Rings, Wiley, New York, 1977.

8.
A. Smoktunowicz, Polynomial rings over nil rings need not be nil, J. Algebra 233 (2000), no. 2, 427-436. crossref(new window)