Geodesic
On Goldie absolute direct summands in modular lattices
Mathematica Bohemica, Tome 148 (2023) no. 2, pp. 243-253
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Absolute direct summand in lattices is defined and some of its properties in modular lattices are studied. It is shown that in a certain class of modular lattices, the direct sum of two elements has absolute direct summand if and only if the elements are relatively injective. As a generalization of absolute direct summand (ADS for short), the concept of Goldie absolute direct summand in lattices is introduced and studied. It is shown that Goldie ADS property is inherited by direct summands. A necessary and sufficient condition is given for an element of modular lattice to have Goldie ADS.
Absolute direct summand in lattices is defined and some of its properties in modular lattices are studied. It is shown that in a certain class of modular lattices, the direct sum of two elements has absolute direct summand if and only if the elements are relatively injective. As a generalization of absolute direct summand (ADS for short), the concept of Goldie absolute direct summand in lattices is introduced and studied. It is shown that Goldie ADS property is inherited by direct summands. A necessary and sufficient condition is given for an element of modular lattice to have Goldie ADS.
DOI : 10.21136/MB.2022.0110-21
Classification : 06B05, 06B99, 06C05
Keywords: injective element; ejective element; Goldie extending element; absolute direct summand; Goldie absolute direct summand 
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Shroff, Rupal. On Goldie absolute direct summands in modular lattices. Mathematica Bohemica, Tome 148 (2023) no. 2, pp. 243-253. doi: 10.21136/MB.2022.0110-21

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