Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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QUOTIENT RINGS INDUCED VIA FUZZY IDEALS

  • Liu, Yong-Lin (Department of Mathematics, Nanping Teachers College) ;
  • Meng, Jie (Department of Mathematics, Northwest University) ;
  • Xin, Xiao-Long (Department of Mathematics, Northwest University)
  • Published : 2001.09.01

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Abstract

This note we give a construction of a quotient ring $R/{\mu}$ induced via a fuzzy ideal ${\mu}$ in a ring R. The Fuzzy First, Second and Third Isomorphism Theorems are established. For some applications of this construction of quotient rings, we show that if ${\mu}$ is a fuzzy ideal of a commutative ring R, then $\mu$ is prime (resp. $R/{\mu}$ is a field, every zero divisor in $R/{\mu}$ is nilpotent). Moreover we give a simpler characterization of fuzzy maximal ideal of a ring.

Keywords

References

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