Displaying similar documents to “Some types of implicative ideals”

On the rhomboidal heredity in ideal lattices

Ladislav Beran (1992)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.

Ojective ideals in modular lattices

Shriram K. Nimbhorkar, Rupal C. Shroff (2015)

Czechoslovak Mathematical Journal

Similarity:

The concept of an extending ideal in a modular lattice is introduced. A translation of module-theoretical concept of ojectivity (i.e. generalized relative injectivity) in the context of the lattice of ideals of a modular lattice is introduced. In a modular lattice satisfying a certain condition, a characterization is given for direct summands of an extending ideal to be mutually ojective. We define exchangeable decomposition and internal exchange property of an ideal in a modular lattice....