The Journal of the Indian Mathematical Society

M. P. Wasadikar ¹, S. K. Nimbhorkar ¹

Affiliations
1 Department of Mathematics, Dr. B. A. M. University, Aurangabad 431004, IN

Abstract

A graph is associated with a poset. If the set of upper bounds of the set of lower bounds of two elements in a poset is the poset itself then we say that these two elements are adjacent in the graph. Properties of this graph are studied. It is shown that if the chromatic number of the associated graph is finite then the clique number is equal to the chromatic number. Some properties of this graph are obtained.

Keywords

Poset, Graph of a Poset, Coloring of a Poset, Clique Number, Chromatic Number, Annihilator.

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S. K. Nimbhorkar ¹, M. P. Wasadikar ¹

Affiliations
1 Department of Mathematics, Dr. B.A.M. University, Aurangabad-431 004, IN

Abstract

A join-semilattice with 0 is called n-normal if every prime ideal contains at most n-minimal prime ideals. In this paper, we obtain some properties and characterizations of n-normal distributive join-semilattices with 0.

Keywords

n-Normal Distributive Join-Semilattice, Prime Ideals, Minimal Prime Ideals, Sectionally n-Normal Semilattice.

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