journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-1624 On simple generalized m-flat rings Ahmad Shaimaa H. Department of Mathematics, College of Computer Sciences and Mathematics, Mosul 41002, University of Mosul, Iraq Mahmood Raida D. Department of Mathematics, College of Computer Sciences and Mathematics, Mosul 41002, University of Mosul, Iraq Mohammed Farah H. Department of Mathematics, College of Computer Sciences and Mathematics, Mosul 41002, University of Mosul, Iraq Ibraheem Zubaida M. Department of Mathematics, College of Computer Sciences and Mathematics, Mosul 41002, University of Mosul, Iraq 26 2 585 590 30 03 2023

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.

 Regular rings m – regular ring GmF – ring NJ – ring Feckly reduced ring access open retracted no