Are zero-symmetric simple nearrings with identity equiprime?

Wen-Fong Ke; Johannes H. Meyer

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 4, page 1289-1298
  • ISSN: 0011-4642

Abstract

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We show that there exist zero-symmetric simple nearrings with identity, which are not equiprime, solving a longstanding open problem.

How to cite

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Ke, Wen-Fong, and Meyer, Johannes H.. "Are zero-symmetric simple nearrings with identity equiprime?." Czechoslovak Mathematical Journal 74.4 (2024): 1289-1298. <http://eudml.org/doc/299641>.

@article{Ke2024,
abstract = {We show that there exist zero-symmetric simple nearrings with identity, which are not equiprime, solving a longstanding open problem.},
author = {Ke, Wen-Fong, Meyer, Johannes H.},
journal = {Czechoslovak Mathematical Journal},
keywords = {nearring with identity; infinite simple group; HNN extension; equiprime nearring; prime radical},
language = {eng},
number = {4},
pages = {1289-1298},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Are zero-symmetric simple nearrings with identity equiprime?},
url = {http://eudml.org/doc/299641},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Ke, Wen-Fong
AU - Meyer, Johannes H.
TI - Are zero-symmetric simple nearrings with identity equiprime?
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 4
SP - 1289
EP - 1298
AB - We show that there exist zero-symmetric simple nearrings with identity, which are not equiprime, solving a longstanding open problem.
LA - eng
KW - nearring with identity; infinite simple group; HNN extension; equiprime nearring; prime radical
UR - http://eudml.org/doc/299641
ER -

References

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  2. Clay, J. R., 10.1007/BF01110428, Math. Z. 104 (1968), 364-371. (1968) Zbl0153.35704MR0224659DOI10.1007/BF01110428
  3. Divinsky, N. J., Rings and Radicals, Mathematical Expositions 14. University of Toronto Press, Toronto (1965). (1965) Zbl0138.26303MR0197489
  4. Higman, G., Neumann, B. H., Neumann, H., 10.1112/jlms/s1-24.4.247, J. Lond. Math. Soc. 24 (1949), 247-254. (1949) Zbl0034.30101MR0032641DOI10.1112/jlms/s1-24.4.247
  5. Kaarli, K., Kriis, T., Prime radical of near-rings, Tartu Riikl. Ül. Toimetised 764 (1987), 23-29 Russian. (1987) Zbl0638.16028MR0913699
  6. Ke, W.-F., Meyer, J. H., Pilz, G. F., Wendt, G., 10.21136/CMJ.2024.0086-24, Czech. Math. J. 74 (2024), 869-880. (2024) MR4804964DOI10.21136/CMJ.2024.0086-24
  7. Meyer, J. H., Matrix Near-Rings: Ph. D. Thesis, University of Stellenbosch, Stellenbosch (1986). (1986) 
  8. Pilz, G., 10.1016/s0304-0208(08)x7135-x, North-Holland Mathematics Studies 23. North-Holland, Amsterdam (1983). (1983) Zbl0521.16028MR0721171DOI10.1016/s0304-0208(08)x7135-x
  9. Veldsman, S., 10.1080/00927879208824479, Commun. Algebra 20 (1992), 2569-2587. (1992) Zbl0795.16034MR1176828DOI10.1080/00927879208824479

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