Generalized extending ideals in modular lattices. (English) Zbl 1351.06004

Nimbhorkar, S. K.; Shroff, Rupal C.

J. Indian Math. Soc., New Ser. 82, No. 3-4, 127-146 (2015).

Authors’ 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.

Reviewer: Marcel Wild (Stellenbosch)

MSC:

06B10	Lattice ideals, congruence relations
06C05	Modular lattices, Desarguesian lattices

Keywords:

modular lattice, extending ideal; \(I\)-jective ideal; generalized extending ideals