1. Objective ideals in modular lattices
- Creator:
- Nimbhorkar, Shriram K. and Shroff, Rupal C.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- modular lattice, essential ideal, max-semicomplement, extending ideal, direct summand, exchangeable decomposition, and ojective ideal
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public