On Goldie absolute direct summands in modular lattices

Rupal Shroff

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 2, page 243-253
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Shroff, Rupal. "On Goldie absolute direct summands in modular lattices." Mathematica Bohemica 148.2 (2023): 243-253. <http://eudml.org/doc/299525>.

@article{Shroff2023,
abstract = {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.},
author = {Shroff, Rupal},
journal = {Mathematica Bohemica},
keywords = {injective element; ejective element; Goldie extending element; absolute direct summand; Goldie absolute direct summand},
language = {eng},
number = {2},
pages = {243-253},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On Goldie absolute direct summands in modular lattices},
url = {http://eudml.org/doc/299525},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Shroff, Rupal
TI - On Goldie absolute direct summands in modular lattices
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 2
SP - 243
EP - 253
AB - 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.
LA - eng
KW - injective element; ejective element; Goldie extending element; absolute direct summand; Goldie absolute direct summand
UR - http://eudml.org/doc/299525
ER -

References

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  8. Nimbhorkar, S. K., Shroff, R. C., 10.21136/MB.2016.0049-14, Math. Bohem. 142 (2017), 163-180. (2017) Zbl1424.06028MR3660173DOI10.21136/MB.2016.0049-14
  9. Quynh, T. C., Şahinkaya, S., 10.24193/subbmath.2018.4.02, Stud. Univ. Babeş-Bolyai, Math. 63 (2018), 437-445. (2018) Zbl1438.16014MR3886059DOI10.24193/subbmath.2018.4.02
  10. Mutlu, F. Takil, On Modules With the Absolute Direct Summand Property: Ph.D. Thesis, University of Anatolia, Eskişehir (2003). (2003) 
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