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Ojective ideals in modular lattices

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431 004, India

    Shriram K. Nimbhorkar & Rupal C. Shroff

Authors
  1. Shriram K. Nimbhorkar
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  2. Rupal C. Shroff
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Correspondence to Shriram K. Nimbhorkar.

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Dedicated to Professor N.K.Thakare and Professor T.T.Raghunathan on the occasion of their 76th birthday

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Nimbhorkar, S.K., Shroff, R.C. Ojective ideals in modular lattices. Czech Math J 65, 161–178 (2015). https://doi.org/10.1007/s10587-015-0166-5

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  • DOI: https://doi.org/10.1007/s10587-015-0166-5

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