IJPAM: Volume 116, No. 2 (2017)

Title

SOME TYPES OF IDEALS IN
DISTRIBUTIVE IMPLICATION GROUPOIDS

Authors

Ravi Kumar Bandaru$^1$, K.P. Shum$^2$, N. Rafi$^3$
$^1$Department of Engineering Mathematics
GITAM University
Hyderabad Campus, Telangana, 502 329, INDIA
$^2$Insititute of Mathematics
Yunnan University
Kunming, 650091, P.R. CHINA
$^3$Department of Mathematics
Bapatla Engineering College
Bapatla, Andhra Pradesh, 522 101, INDIA

Abstract

In this paper, the notions of $\mathcal{I}-$ideal, $\mathcal{N}-$ideal and $\mathcal{F}$-ideal in a distributive implication groupoid are introduced and proved that these notions are equivalent. Also, we introduced the notion of $\mathcal{O}-$ideal and maximal ideal in a distributive implication groupiod and studied the relation between $\mathcal{O}-$ideal and $\mathcal{N}-$ideal. Finally, we shown that $\mathcal{O}-$ideals and maximal ideals are equivalent.

History

Received: 2017-04-06
Revised: 2017-06-28
Published: October 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 06F35, 20N02
Key Words and Phrases: $\mathcal{I}-$ideal, $\mathcal{N}-$ideal, $\mathcal{F}$-ideal, $\mathcal{O}-$ideal

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Bibliography

1
D. Buşneag, A note on deductive systems of a Hilbert algebra, Kobe Journal of Mathematics, Vol.2(1985), 29-35.

2
R.K.Bandaru, On ideals of implication groupoids, Advances in Decision Sciences, Vol.2012, Article ID 652814, 9 pages, 2012.

3
R.K.Bandaru and K.P.Shum, Vague ideals of implication groupoids, Discussion Math. General Algebra and applications,33(2013), 221222.

4
R.K.Bandaru and K.P.Shum, Implicative and fuzzy implicative ideals of distributive implication groupoids, Journal of Mathematical Research with Applications, 34(6)(2014), 631639.

5
R.K.Bandaru, K.P.Shum and N.Rafi, Fuzzy Ideals of Implication Groupoids, Italian Journal of Pure and Applied Mathematics, 34(2015), 277-290.

6
R.K.Bandaru and B. Davvaz, On Fuzzy Implication Groupoids, The Journal of Fuzzy Mathematics, 23(1)(2015), 141-148.

7
I. Chajda and R. Halas , Congruences and ideals in Hilbert algebras. Kyungpook Math. J. 39 (1999), 429-43

8
I. Chajda and R. Halas, Distributive and implication groupoids, Central European Journal of Mathematics 5(3) (2007), 484-49.

9
S. Celani, A note on homomorphisms of Hilbert algebras, International Journal of Mathematics and Mathematical Sciences, Vol.29(1)(2002), 55-61.

10
A. Diego, Sur les algebres de Hilbert, Collection de Logique Mathematique, Edition Hermann, Serie A, XXI, 1966.

11
S.M.Hong and Y.B. Jun, On deductive systems of Hilbert algebras, Comm. Korean Math. Soc., Vol.11(3)(1996), 595-600.

12
Y. B. Jun, Commutative Hilbert Algebras, Soochow Journal of Mathematics, Vol.22(4)(1996), 477-484.

How to Cite?

DOI: 10.12732/ijpam.v116i2.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 2
Pages: 377 - 384


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