Informatics Publishing Limited

S. K. Nimbhorkar ¹, Rupal C. Shroff ²

Affiliations
1 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, IN
2 Department of Core Engineering and Engineering Sciences, MIT College of Engineering, Pune 411038, IN

Abstract

The concept of an extending ideal and that of I-jectivity for an ideal in a lattice is introduced. It is shown that in a modular lattice, the direct sum of extending ideals is extending if and only if the ideals are relatively jective. We also define a generalized extending ideal in a lattice and obtain some properties and characterizations of such ideals in a modular lattice.

Keywords

Extending Ideal, I-Jective Ideal and Generalized Extending Ideals.

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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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