Prime submodules and maximal submodules in the idealization of a module

Authors

  • Alex Molina Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Ciudad Universitaria, Lima, Perú.
  • Mario Santiago Facultad de Ciencias Matem\'aticas, Universidad Nacional Mayor de San Marcos
  • Juan Villanueva Instituto de Ciencias Exatas e da Terra, Campus Universitário do Araguaia, Universidade Federal de Mato Grosso, 78605-091, Barra do Garcas, MT, Brasil.

DOI:

https://doi.org/10.17268/sel.mat.2024.01.03

Keywords:

rings, prime spectrun of a module, modules, maximal submodule, prime submodule

Abstract

This paper describes certain types of prime submodules and maximal submodules that are found within the idealization of a module. As a consequence of this, it is concluded that every module over a commutative ring with identity element has an extension whose prime spectrum is nonempty.

References

Dauns J. Prime modules. Journal für die reine und angewandte Mathematika. 1978;298:156-81.

Lu CP. Prime submodules of modules. Commentarii mathematici Universitatis Sancti Pauli.

;33(1):61-9.

Lu CP. Spectra of modules. Communications in Algebra. 1995;23(10):3741-52.

McCasland RL, Moore ME. Prime submodules. Communications in Algebra. 1992;20(6):1803-17.

Lu CP. The Zariski topology on the prime spectrum of a module. Houston Journal of Mathematics. 1999;25(3):417-32.

Duraivel T. Topology on spectrum of modules. Journal of the Ramanujan Mathematical Society. 1994;9(1):25-34.

Nagata M. Local rings. New York: Robert E. Krieger Publishing Company; 1975.

Anderson DD, Winders M. Idealization of a module. Journal of Commutative Algebra. 2009;1(1):3-56.

Jenkins J, Smith PF. On the prime radical of a module over a commutative ring. Communications in Algebra. 1992;20(12):3593-602.

Molina A, Santiago M, Villanueva J. On the prime spectrum of Z-module ZxZ. Sometido para publicación. 2024:15 pp.

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Published

2024-07-29

How to Cite

Molina, A., Santiago, M., & Villanueva, J. (2024). Prime submodules and maximal submodules in the idealization of a module. Selecciones Matemáticas, 11(01), 30 - 41. https://doi.org/10.17268/sel.mat.2024.01.03

Issue

Vol. 11 No. 01 (2024): January - July

Section

Articles

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