### Abstract

We investigate the radical structure of a fuzzy polynomial ideal induced by a fuzzy ideal of a ring and study its properties. Given a fuzzy ideal β of R and a homomorphism f: R → R ′, we show that if f x is the induced homomorphism of f, that is, f x (i = 0 n a i x i) = i = 0 n f (a i) x i, then f x - 1 [ (β) x ] = (f - 1 (β)) x.

Original language | English |
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Article number | 7821678 |

Journal | Discrete Dynamics in Nature and Society |

Volume | 2016 |

DOIs | |

State | Published - 2016 Jan 1 |

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### Cite this

*Discrete Dynamics in Nature and Society*,

*2016*, [7821678]. https://doi.org/10.1155/2016/7821678

}

*Discrete Dynamics in Nature and Society*, vol. 2016, 7821678. https://doi.org/10.1155/2016/7821678

**Radical Structures of Fuzzy Polynomial Ideals in a Ring.** / Kim, Hee Sik; Kim, Chang Bum; So, Keum Sook.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Radical Structures of Fuzzy Polynomial Ideals in a Ring

AU - Kim, Hee Sik

AU - Kim, Chang Bum

AU - So, Keum Sook

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We investigate the radical structure of a fuzzy polynomial ideal induced by a fuzzy ideal of a ring and study its properties. Given a fuzzy ideal β of R and a homomorphism f: R → R ′, we show that if f x is the induced homomorphism of f, that is, f x (i = 0 n a i x i) = i = 0 n f (a i) x i, then f x - 1 [ (β) x ] = (f - 1 (β)) x.

AB - We investigate the radical structure of a fuzzy polynomial ideal induced by a fuzzy ideal of a ring and study its properties. Given a fuzzy ideal β of R and a homomorphism f: R → R ′, we show that if f x is the induced homomorphism of f, that is, f x (i = 0 n a i x i) = i = 0 n f (a i) x i, then f x - 1 [ (β) x ] = (f - 1 (β)) x.

UR - http://www.scopus.com/inward/record.url?scp=84962839009&partnerID=8YFLogxK

U2 - 10.1155/2016/7821678

DO - 10.1155/2016/7821678

M3 - Article

AN - SCOPUS:84962839009

VL - 2016

JO - Discrete Dynamics in Nature and Society

JF - Discrete Dynamics in Nature and Society

SN - 1026-0226

M1 - 7821678

ER -