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Nimbhorkar, Shriram K.; Shroff, Rupal C.

Ojective ideals in modular lattices. (English) Zbl 1338.06004

Czech. Math. J. 65, No. 1, 161-178 (2015).
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.
Reviewer: Yuri Movsisyan (Yerevan)

Cited in 2 Documents

MSC:

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

Keywords:

modular lattices; lattices of ideals; essential ideals; extending ideals; direct summands; exchangeable decompositions; ojective ideals
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References:

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