The Journal of the Indian Mathematical Society

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.

Full Text