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Keywords:
nearring with identity; infinite simple group; HNN extension; equiprime nearring; prime radical
nearring with identity; infinite simple group; HNN extension; equiprime nearring; prime radical
Summary:
We show that there exist zero-symmetric simple nearrings with identity, which are not equiprime, solving a longstanding open problem.
References:
[1] Booth, G. L., Groenewald, N. J., Veldsman, S. A.: A Kurosh-Amitsur prime radical for near-rings. Commun. Algebra 18 (1990), 3111-3122. DOI 10.1080/00927879008824063 | MR 1063353 | Zbl 0706.16025
[2] Clay, J. R.: The near-rings on groups of low order. Math. Z. 104 (1968), 364-371. DOI 10.1007/BF01110428 | MR 0224659 | Zbl 0153.35704
[3] Divinsky, N. J.: Rings and Radicals. Mathematical Expositions 14. University of Toronto Press, Toronto (1965). MR 0197489 | Zbl 0138.26303
[4] Higman, G., Neumann, B. H., Neumann, H.: Embedding theorems for groups. J. Lond. Math. Soc. 24 (1949), 247-254. DOI 10.1112/jlms/s1-24.4.247 | MR 0032641 | Zbl 0034.30101
[5] Kaarli, K., Kriis, T.: Prime radical of near-rings. Tartu Riikl. Ül. Toimetised 764 (1987), 23-29 Russian. MR 0913699 | Zbl 0638.16028
[6] Ke, W.-F., Meyer, J. H., Pilz, G. F., Wendt, G.: On zero-symmetric nearrings with identity whose additive groups are simple. Czech. Math. J. 74 (2024), 869-880. DOI 10.21136/CMJ.2024.0086-24 | MR 4804964
[7] Meyer, J. H.: Matrix Near-Rings: Ph. D. Thesis. University of Stellenbosch, Stellenbosch (1986).
[8] Pilz, G.: Near-Rings: The Theory and Its Applications. North-Holland Mathematics Studies 23. North-Holland, Amsterdam (1983). DOI 10.1016/s0304-0208(08)x7135-x | MR 0721171 | Zbl 0521.16028
[9] Veldsman, S.: On equiprime near-rings. Commun. Algebra 20 (1992), 2569-2587. DOI 10.1080/00927879208824479 | MR 1176828 | Zbl 0795.16034
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