Geodesic
Ojective ideals in modular lattices
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 161-178
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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.
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.
DOI : 10.1007/s10587-015-0166-5
Classification : 06B10, 06C05, 16D10
Keywords: modular lattice; essential ideal; max-semicomplement; extending ideal; direct summand; exchangeable decomposition; ojective ideal 
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Nimbhorkar, Shriram K.; Shroff, Rupal C. Ojective ideals in modular lattices. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 161-178. doi: 10.1007/s10587-015-0166-5

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