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 Algebra Discrete Math., 2013, Volume 16, Issue 1, Pages 61–70 (Mi adm434)  RESEARCH ARTICLE

$(\lambda,\mu)$-fuzzy interior ideals of ordered $\Gamma$-semigroups

Yuming Fengab, P. Corsinia

a Dipartimento di Ingegneria Civile e Architettura dell’Universita’ degli Studi di Udine, Via delle Scienze, 206, 33100 Udine, Italy
b School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, P.R. China

Abstract: For all $\lambda,\mu\in [0,1]$ such that $\lambda<\mu$, we first introduced the definitions of $(\lambda,\mu)$-fuzzy ideals and $(\lambda,\mu)$-fuzzy interior ideals of an ordered $\Gamma$-semigroup. Then we proved that in regular and in intra-regular ordered semigroups the $(\lambda,\mu)$-fuzzy ideals and the $(\lambda,\mu)$-fuzzy interior ideals coincide. Lastly, we introduced the concept of a $(\lambda,\mu)$-fuzzy simple ordered $\Gamma$-semigroup and characterized the simple ordered $\Gamma$-semigroups in terms of $(\lambda,\mu)$-fuzzy interior ideals.

Keywords: $\Gamma$-semigroup; $(\lambda,\mu)$-fuzzy interior ideal; $(\lambda,\mu)$-fuzzy simple; regular ordered $\Gamma$-semigroup; intra-regular ordered $\Gamma$-semigroup. Full text: PDF file (174 kB) References: PDF file   HTML file

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Citation: Yuming Feng, P. Corsini, “$(\lambda,\mu)$-fuzzy interior ideals of ordered $\Gamma$-semigroups”, Algebra Discrete Math., 16:1 (2013), 61–70 Citation in format AMSBIB
\Bibitem{FenCor13} \by Yuming~Feng, P.~Corsini \paper $(\lambda,\mu)$-fuzzy interior ideals of ordered $\Gamma$-semigroups \jour Algebra Discrete Math. \yr 2013 \vol 16 \issue 1 \pages 61--70 \mathnet{http://mi.mathnet.ru/adm434} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184698} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000342623000004} 

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This publication is cited in the following articles:
1. A. R. Shabani, H. Rasouli, “On $\Gamma$-biacts and their Green's relations”, Ital. J. Pure Appl. Math., 2017, no. 37, 409–418  2. M. Y. Abbasi, A. Basar, A. F. Talee, S. A. Khan, “Generalized ($(\xi,\zeta)$-)soft interior $\Gamma$-hyperideals of $\Gamma$-semihypergroups”, Honam Math. J., 40:1 (2018), 93–108    •  Contact us: math-net2020_04 [at] mi-ras ru Terms of Use Registration Logotypes © Steklov Mathematical Institute RAS, 2020