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Year 2020, , 229 - 229, 14.07.2020

Gabriel Pıcavet Martine Pıcavet-l'hermıtte

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, , 229 - 229, 14.07.2020

Gabriel Pıcavet Martine Pıcavet-l'hermıtte

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. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

Keywords

Idealization minimal ring extension subintegral extension

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.
There are 2 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Gabriel Pıcavet This is me

Martine Pıcavet-l'hermıtte This is me

Publication Date July 14, 2020
Published in Issue Year 2020

Cite

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. 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. July 2020;28(28):229-229. doi:10.24330/ieja.768272
Chicago Pıcavet, Gabriel, and Martine Pıcavet-l’hermıtte. “AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES”. International Electronic Journal of Algebra 28, no. 28 (July 2020): 229-29. https://doi.org/10.24330/ieja.768272.
EndNote Pıcavet G, Pıcavet-l’hermıtte M (July 1, 2020) AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES. International Electronic Journal of Algebra 28 28 229–229.
IEEE G. Pıcavet and M. Pıcavet-l’hermıtte, “AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES”, IEJA, vol. 28, no. 28, pp. 229–229, 2020, doi: 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.
JAMA Pıcavet G, Pıcavet-l’hermıtte M. AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES. IEJA. 2020;28:229–229.
MLA Pıcavet, Gabriel and Martine Pıcavet-l’hermıtte. “AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES”. International Electronic Journal of Algebra, vol. 28, no. 28, 2020, pp. 229-, doi:10.24330/ieja.768272.
Vancouver Pıcavet G, Pıcavet-l’hermıtte M. AN ADDENDUM TO THE PAPER: MODULES WITH FINITELY MANY SUBMODULES. IEJA. 2020;28(28):229-.