Article
| Title: | Are zero-symmetric simple nearrings with identity equiprime? (English) |
| Author: | Ke, Wen-Fong |
| Author: | Meyer, Johannes H. |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 4 |
| Year: | 2024 |
| Pages: | 1289-1298 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We show that there exist zero-symmetric simple nearrings with identity, which are not equiprime, solving a longstanding open problem. (English) |
| Keyword: | nearring with identity |
| Keyword: | infinite simple group |
| Keyword: | HNN extension |
| Keyword: | equiprime nearring |
| Keyword: | prime radical |
| MSC: | 16N60 |
| MSC: | 16N80 |
| MSC: | 16Y30 |
| MSC: | 20E06 |
| MSC: | 20E32 |
| DOI: | 10.21136/CMJ.2024.0302-24 |
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| Date available: | 2024-12-15T06:42:23Z |
| Last updated: | 2024-12-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152702 |
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| Reference: | [2] Clay, J. R.: The near-rings on groups of low order.Math. Z. 104 (1968), 364-371. Zbl 0153.35704, MR 0224659, 10.1007/BF01110428 |
| Reference: | [3] Divinsky, N. J.: Rings and Radicals.Mathematical Expositions 14. University of Toronto Press, Toronto (1965). Zbl 0138.26303, MR 0197489 |
| Reference: | [4] Higman, G., Neumann, B. H., Neumann, H.: Embedding theorems for groups.J. Lond. Math. Soc. 24 (1949), 247-254. Zbl 0034.30101, MR 0032641, 10.1112/jlms/s1-24.4.247 |
| Reference: | [5] Kaarli, K., Kriis, T.: Prime radical of near-rings.Tartu Riikl. Ül. Toimetised 764 (1987), 23-29 Russian. Zbl 0638.16028, MR 0913699 |
| Reference: | [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. MR 4804964, 10.21136/CMJ.2024.0086-24 |
| Reference: | [7] Meyer, J. H.: Matrix Near-Rings: Ph. D. Thesis.University of Stellenbosch, Stellenbosch (1986). |
| Reference: | [8] Pilz, G.: Near-Rings: The Theory and Its Applications.North-Holland Mathematics Studies 23. North-Holland, Amsterdam (1983). Zbl 0521.16028, MR 0721171, 10.1016/s0304-0208(08)x7135-x |
| Reference: | [9] Veldsman, S.: On equiprime near-rings.Commun. Algebra 20 (1992), 2569-2587. Zbl 0795.16034, MR 1176828, 10.1080/00927879208824479 |
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