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Year 2020, Volume 28, Issue 28, 229 - 229, 14.07.2020
https://doi.org/10.24330/ieja.768272

Abstract

References

  • D. D. Anderson and S. Chun, Commutative rings with finitely generated monoids of fractional ideals, J. Algebra, 320 (2008), 3006-3021.
  • G. Picavet and M. Picavet-L'Hermitte, Modules with finitely many submodules, Int. Electron. J. Algebra, 19 (2016), 119-131.

AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES

Year 2020, Volume 28, Issue 28, 229 - 229, 14.07.2020
https://doi.org/10.24330/ieja.768272

Abstract

Abstract of the paper: "G. Picavet and M. Picavet-L'Hermitte, Modules with finitely many submodules, Int. Electron. J. Algebra, 19 (2016), 119-131.":

We characterize ring extensions $R \subset S$ having FCP (FIP), where $S$ is the idealization of some $R$-module. As a by-product we exhibit characterizations of the modules that have finitely many submodules. Our tools are minimal ring morphisms, while Artinian conditions on rings are ubiquitous. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

References

  • D. D. Anderson and S. Chun, Commutative rings with finitely generated monoids of fractional ideals, J. Algebra, 320 (2008), 3006-3021.
  • G. Picavet and M. Picavet-L'Hermitte, Modules with finitely many submodules, Int. Electron. J. Algebra, 19 (2016), 119-131.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Gabriel PICAVET This is me (Primary Author)
Mathematiques, 8 Rue du Forez
France


Martine PICAVET-L'HERMITTE This is me
Mathematiques, 8 Rue du Forez
France

Publication Date July 14, 2020
Published in Issue Year 2020, Volume 28, Issue 28

Cite

Bibtex @note { ieja768272, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2020}, volume = {28}, number = {28}, pages = {229 - 229}, doi = {10.24330/ieja.768272}, title = {AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES}, key = {cite}, author = {Pıcavet, Gabriel and Pıcavet-l'hermıtte, Martine} }
APA Pıcavet, G. & Pıcavet-l'hermıtte, M. (2020). AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES . International Electronic Journal of Algebra , 28 (28) , 229-229 . DOI: 10.24330/ieja.768272
MLA Pıcavet, G. , Pıcavet-l'hermıtte, M. "AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES" . International Electronic Journal of Algebra 28 (2020 ): 229-229 <https://dergipark.org.tr/en/pub/ieja/issue/55997/768272>
Chicago Pıcavet, G. , Pıcavet-l'hermıtte, M. "AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES". International Electronic Journal of Algebra 28 (2020 ): 229-229
RIS TY - JOUR T1 - AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES AU - GabrielPıcavet, MartinePıcavet-l'hermıtte Y1 - 2020 PY - 2020 N1 - doi: 10.24330/ieja.768272 DO - 10.24330/ieja.768272 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 229 EP - 229 VL - 28 IS - 28 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.768272 UR - https://doi.org/10.24330/ieja.768272 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Algebra AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES %A Gabriel Pıcavet , Martine Pıcavet-l'hermıtte %T AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES %D 2020 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 28 %N 28 %R doi: 10.24330/ieja.768272 %U 10.24330/ieja.768272
ISNAD Pıcavet, Gabriel , Pıcavet-l'hermıtte, Martine . "AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES". International Electronic Journal of Algebra 28 / 28 (July 2020): 229-229 . https://doi.org/10.24330/ieja.768272
AMA Pıcavet G. , Pıcavet-l'hermıtte M. AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES. IEJA. 2020; 28(28): 229-229.
Vancouver Pıcavet G. , Pıcavet-l'hermıtte M. AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES. International Electronic Journal of Algebra. 2020; 28(28): 229-229.
IEEE G. Pıcavet and M. Pıcavet-l'hermıtte , "AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES", International Electronic Journal of Algebra, vol. 28, no. 28, pp. 229-229, Jul. 2020, doi:10.24330/ieja.768272