The Journal of the Indian Mathematical Society

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Generalized Extending Ideals in Modular Lattices


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

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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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  • Generalized Extending Ideals in Modular Lattices

Abstract Views: 253  |  PDF Views: 5

Authors

S. K. Nimbhorkar
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India
Rupal C. Shroff
Department of Core Engineering and Engineering Sciences, MIT College of Engineering, Pune 411038, India

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.