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ON ONE-SIDED IDEAL STRUCTURE OF RINGS IN WHICH EVERY PROPER IDEAL IS PRIME
Keywords:
fully prime, right boundedDOI:
https://doi.org/10.17654/0972555525001Abstract
The structure of rings in which every proper ideal is prime has been studied, for example, in [1] and [2]. In this paper, we investigate right ideal structure in such rings and link to conditions under which such rings are simple rings.
Received: September 3, 2024
Revised: October 8, 2024
Accepted: October 30, 2024
References
J. A. Beachy and M. Medina-Bárcenas, Fully prime modules and fully semiprime modules, Bull. Korean Math. Soc. 57(5) (2020), 1177-1193.
W. D. Blair and H. Tsutsui, Fully prime rings, Comm. Algebra 22(13) (1994), 5389-5400.
R. C. Courter, Rings all of whose factor rings are semi-prime, Canad. Math. Bull. 12 (1969), 417-426.
Y. Hirano, On rings all of whose factor rings are integral domain, J. Austral. Math. Soc. (Series A) 55 (1993), 325-333.
K. Koh, On one sided ideals of a prime type, Proc. Amer. Math. Soc. 28 (1976), 321-329.
R. Mazurek and E. Roszkowska, Example of chain domains, Proc. Amer. Math. Soc. 126(3) (1998), 661-667.
V. S. Ramamurthi, Weakly regular rings, Canad. Math. Bull. 16(3) (1973), 317-321.
L. Rowen, Ring Theory, Academic Press, Boston, Volume 1, 1988.
H. Tominaga, On s-unital rings, Math. J. Okayama Univ. 18 (1976), 117-134.
H. Tsutsui, Fully prime rings. II, Comm. Algebra 24 (1996), 2981-2989.
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