On simple generalized m-flat rings

Ahmad, Shaimaa H.; Mahmood, Raida D.; Mohammed, Farah H.; Ibraheem, Zubaida M.

doi:10.47974/JDMSC-1624

Open Access Research Article

On simple generalized m-flat rings

^*Shaimaa H. AhmadCorresponding authorshaymaahatim@uomosul.edu.iqDepartment of MathematicsCollege of Computer Sciences and MathematicsMosul 41002University of MosulIraqView full profile → , Raida D. Mahmoodraida.1961@uomosul.edu.iqDepartment of MathematicsCollege of Computer Sciences and MathematicsMosul 41002University of MosulIraqView full profile → , Farah H. Mohammedfarahalkadoo@uomosul.edu.iqDepartment of MathematicsCollege of Computer Sciences and MathematicsMosul 41002University of MosulIraqView full profile → , Zubaida M. Ibraheemz.mohammed@uomosul.edu.iqDepartment of MathematicsCollege of Computer Sciences and MathematicsMosul 41002University of MosulIraqView full profile →

* Corresponding author · click or hover a name for details

pp. 585–590Vol. 26Issue 2March 2022DOI: 10.47974/JDMSC-1624 Crossmark XML

Received:: 05 Aug 2021
Accepted:: 05 Feb 2022
Published Online:: 30 Mar 2023
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1624
Pages:: 585–590

Abstract

A ring N is known as a right (left) SGmF – ring, if each simple right (left) N -modules are Gm – Flat. In this paper, we investigate characterizations of SGmF – ring. And from the results: 1. If N is a semi-prime, and right SGmF–ring, then the C(N) is regular ring. 2. If N is SGmF – ring, with every ideal of N is principal then: a. N is NJ iff N is feckly reduced, b. N is m – regular ring, if N is ZC ring.

Keywords

Regular rings m – regular ring GmF – ring NJ – ring Feckly reduced ring

Subject Classifications

20M1204A72

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