PRIME IDEALS IN STRUCTURAL MATRIX NEAR-RINGS
Keywords:Near-rings, prime ideals, matrix near-rings
This paper studies different types of prime ideals and their radicals in structural matrix near-rings. Relationships between various types of prime ideals of a near-ring and the corresponding structural matrix near-ring are given.
G. L. Booth and N. J. Groenewald, "On primeness in matrix near-rings," Arch. Math., 56 (1991), 539-546.
G. L. Booth, N.'J . Groenewald, and S. Veldsman, "A Kurosh-Amitsur prime radical for near-rings," Comm. Alg., 18 (1990),. 3111-3122.
J. R. Clay, Nearrings: Geneses and Applications, Oxford Science Publications, Oxford, New York, Tokyo, 1992.
N. J. Groenewald, "Different prime ideals in near-rings," Comm. Alg., 19 (1991), 2667-2675
H. E. Heatherly, "Matrix near-rings," J. London Math. Soc., 7 (1973), 355-356.
S. Ligh, "A note on matrix near-rings," J. London Math. Soc., 11 (1975), 383-384
J. D. P. Meldrum, Near-Rings and Their Links with Groups, Pitman, Marshfield, M. A., 1985
—and J. H. Meyer, "Modules over matrix near-rings and the Jo-radical," Monatsh. Math., 112 (1991), 125-139.
—- and A. P. J. van der Walt, "Matrix near-rings," Arch. Math. 47 (1986), 312-319.
G. Pilz, Near-Rings, 2nd. edition, North-Holland, Amsterdam, 1983
A. P. J. van der Walt and L. van Wyk, "The h -radical in structural matrix near-rings," J. Algebra, 123 (1989), 248-261.
L. van Wyk, "The 2-primitive ideals of structural matrix near-rings," Proc. Edinburgh Math. Soc., 34 (1991), 229-239.
— , "Maximal left ideals in structural matrix rings," Comm. Alg. 16 (1988), 399-419.
S. Veldsman, "Special radicals and matrix near-rings," J. Austral. Math. Soc. (Series A), 52 (1992), 356-367.
How to Cite
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.