Keywords:-

Keywords: Almost Distributive Lattice (ADL); associative ADL; pseudo-complementation; congruence on pseudo-complemented ADL; subdirectly irreducible ADL.

Article Content:-

Abstract

We introduce the concept of congruence on pseudo-complemented ADL's and study on certain properties of these. Mainly, in this paper all subdirectly irreducible pseudo-complemented ADL's are characterized.

References:-

References

G. Birkhoff, Lattice Theory, Vol. 25 Amer. Math. Soc., Colluquim Pub-

lications, 1967.

T. S. Blyth, Ideals and filters of pseudo-complemented semilattices,Proc.

Edinburgh Math. Soc. 23 (1980) 301-316.

S. Burris and H. P. Sankappanavar, A course in Universal algebra,

Springer - Verlag, Newyork, 1980.

W. H. Cornish, Congruences on distributive pseudo-complemented lattices,

Bull. Austral. Math. Soc. 8 (1973) 161-179.

O. Frink, Pseudo-complementes in semilattices, Duke Math. J., Vol. 29

(1961), 505 -514.

G. C. Rao and M. Sambasivarao, Annihilator Ideals in Almost Distributive

Lattices, International Mathematical Forum, Vol. 4 (2009), no 15,

-746.

Ch. Santhi Sundar Raj, B. Venkateswarlu and R. Vasu Babu, The

Stonity of a pseudo-complemented ADL, Asian-European Journal of

Mathematics., Vol. 7, No. 3(2014).

U. M. Swamy and G. C. Rao, Almost Distributive Lattices, J. Australian

Math. Soc., (Series A), Vol. 31 (1981), 77- 91.

U. M. Swamy, G. C. Rao and G. N. Rao, Pseudo complementation

on Almost Distributive Lattices, Southeast Asian Bull. Math., Vol. 24

(2000), 95-104.

U. M. Swamy, G.C. Rao and G.N. Rao, Stone Almost Distributive Lattices,

Southeast Asian Bulletin of Mathematics, Vol.27(2003), 513-526.

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Raj, C. S. S., & Santhi, M. (2016). SUBDIRECTLY IRREDUCIBLE PSEUDO-COMPLEMENTED ADL’S. International Journal Of Mathematics And Computer Research, 4(11), 1659-1669. Retrieved from http://ijmcr.in/index.php/ijmcr/article/view/80