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PRIME RADICALS OF SKEW LAURENT POLYNOMIAL RINGS

  • Published : 2005.08.01

Abstract

Let R be a ring with an automorphism 17. An ideal [ of R is ($\sigma$-ideal of R if $\sigma$(I).= I. A proper ideal P of R is ($\sigma$-prime ideal of R if P is a $\sigma$-ideal of R and for $\sigma$-ideals I and J of R, IJ $\subseteq$ P implies that I $\subseteq$ P or J $\subseteq$ P. A proper ideal Q of R is $\sigma$-semiprime ideal of Q if Q is a $\sigma$-ideal and for a $\sigma$-ideal I of R, I$^{2}$ $\subseteq$ Q implies that I $\subseteq$ Q. The $\sigma$-prime radical is defined by the intersection of all $\sigma$-prime ideals of R and is denoted by P$_{(R). In this paper, the following results are obtained: (1) For a principal ideal domain R, P$_{(R) is the smallest $\sigma$-semiprime ideal of R; (2) For any ring R with an automorphism $\sigma$ and for a skew Laurent polynomial ring R[x, x$^{-1}$; $\sigma$], the prime radical of R[x, x$^{-1}$; $\sigma$] is equal to P$_{(R)[x, x$^{-1}$; $\sigma$ ].

Keywords

sigma-semiprime ring;sigma-prime ring;sigma-prime radical;skew Laurent polynomial rin

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Cited by

  1. On primeness of general skew inverse Laurent series ring vol.45, pp.3, 2017, https://doi.org/10.1080/00927872.2016.1172595
  2. Some Results On Prime Skew Rings vol.40, pp.2, 2012, https://doi.org/10.1080/00927872.2010.538104