Mathematics and Statistics Vol. 2(3), pp. 105 - 109
DOI: 10.13189/ms.2014.020301
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On N-Fold Positive Implicative Artinian and Positive Implicative Notherian BCK-Algebras

B. Satyanarayana ¹, R. Durga Prasad ^1,*, L. Krishna ^2
1 Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar-522 510, Andhra Pradesh, India
² Department of Mathematics, Acharya Nagarjuna University Campus Ongole, Ongole-523 002, Andhra Pradesh, India

ABSTRACT

The notion of BCK-algebras was initiated by Imai and Iseki in 1966 as a genera-lization of both classical and non-classical posi-tional calculus. In 1999, Huang and Chen introduced the notion of n-fold positive implicative ideals in BCK-algebras. In 2011, Satyanarayana and Durga Prasad introduced foldness of intuitionistic fuzzy positive implicative ideals in BCK-algebras. In this paper, we introduce the notion of n-fold positive implicative ideals, n-fold positive implicative Artinian (shortly, PIⁿ -Artinian) and n-fold positive implicative Noe-therian (shortly, PIⁿ-Noetherian) BCK-algebras and study some of its properties.

KEYWORDS
BCK-Algebras, N-Fold Positive Implicative Ideal, Artinian and Noetherian BCK-Algebras

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] B. Satyanarayana , R. Durga Prasad , L. Krishna , "On N-Fold Positive Implicative Artinian and Positive Implicative Notherian BCK-Algebras," Mathematics and Statistics, Vol. 2, No. 3, pp. 105 - 109, 2014. DOI: 10.13189/ms.2014.020301.

(b). APA Format:
B. Satyanarayana , R. Durga Prasad , L. Krishna (2014). On N-Fold Positive Implicative Artinian and Positive Implicative Notherian BCK-Algebras. Mathematics and Statistics, 2(3), 105 - 109. DOI: 10.13189/ms.2014.020301.