Ojective ideals in modular lattices

Shriram K. Nimbhorkar; Rupal C. Shroff

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 1, page 161-178
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Nimbhorkar, Shriram K., and Shroff, Rupal C.. "Ojective ideals in modular lattices." Czechoslovak Mathematical Journal 65.1 (2015): 161-178. <http://eudml.org/doc/270038>.

@article{Nimbhorkar2015,
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.},
author = {Nimbhorkar, Shriram K., Shroff, Rupal C.},
journal = {Czechoslovak Mathematical Journal},
keywords = {modular lattice; essential ideal; max-semicomplement; extending ideal; direct summand; exchangeable decomposition; ojective ideal; modular lattices; lattices of ideals; essential ideals; extending ideals; direct summands; exchangeable decompositions; ojective ideals},
language = {eng},
number = {1},
pages = {161-178},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ojective ideals in modular lattices},
url = {http://eudml.org/doc/270038},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Nimbhorkar, Shriram K.
AU - Shroff, Rupal C.
TI - Ojective ideals in modular lattices
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 161
EP - 178
AB - 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.
LA - eng
KW - modular lattice; essential ideal; max-semicomplement; extending ideal; direct summand; exchangeable decomposition; ojective ideal; modular lattices; lattices of ideals; essential ideals; extending ideals; direct summands; exchangeable decompositions; ojective ideals
UR - http://eudml.org/doc/270038
ER -

References

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