Ojective ideals in modular lattices. (English) Zbl 1338.06004

In this paper 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. It is shown that a finite decomposition of an extending ideal is exchangeable if and only if its summands are mutually ojective.


06B10 Lattice ideals, congruence relations
06C05 Modular lattices, Desarguesian lattices
16D50 Injective modules, self-injective associative rings
06B05 Structure theory of lattices
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