A NOTE ON -QUASI-IDEALS IN RINGS

Ronnason Chinram (Thailand)

Received June 17, 2008

References:

[1] R. Chinram and Y. Kemprasit, The intersection property of quasi-ideals in generalized rings of strictly upper triangular matrices, East-West J. Math. 2 (2001), 201-210. [2] R. Chinram and Y. Kemprasit, Minimal quasi-ideals of generalized rings of linear transformations, Pure Math. Appl. 13 (2003), 317-324. [3] R. Chinram and Y. Kemprasit, Some generalized rings of upper triangular matrices having the intersection property of quasi-ideals, East-West J. Math. Special Volume (2004), 25-32. [4] R. Chinram and Y. Kemprasit, Minimal quasi-ideals and minimal bi-ideals in generalized rings of strictly upper triangular matrices, Thai J. Math. 3 (2005), 1-6. [5] R. Chinram and C. Rungsaripipat, The intersection property of quasi-ideals in rings of strictly upper triangular matrices over Adv. Algebra Anal. 1 (2006), 123-131. [6] Y. Kemprasit and R. Chinram, Generalized rings of linear transformations having the intersection property of quasi-ideals, Vietnam J. Math. 30 (2002), 283-288. [7] O. Steinfeld, On ideal-quotients and prime ideals, Acta Math. Acad. Sci. Hungar. 4 (1953), 289-298. [8] O. Steinfeld, Quasi-ideals in Rings and Semigroups, Akadémiai Kiadó, Budapest, 1978. [9] J. von Neumann, On regular rings, Proc. Nat. Acad. Sci. U.S.A., 22 (1936), 707-713. [10] H. J. Weinert, On quasi-ideals in rings, Acta Math. Hungar. 43 (1984), 85-99. [11] M. C. Zhang, Y. Q. Chen and Y. H. Li, The intersection property of quasi-ideals in rings and semigroup rings, Southeast Asian Bull. Math. 20 (1996), 117-122.

Keywords and phrases: quasi-ideals, m-left ideal, n-right ideals, -quasi-ideals.