On Nilpotent Rings of Order $p^4$ with Some Additional Properties
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 3, pp. 53-69
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In this paper, indecomposable nilpotent rings of order $p^4$ and of index $3$ satisfied the identity $x^2=0$ have been described. Moreover, indecomposable nilpotent rings of order $p^4$ and of index $3$ that have an element of additive order $p^t$ ($t\in\{3,4\}$) have been classified.
Keywords: finite ring, nilpotent ring.
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A. S. Kuzmina. On Nilpotent Rings of Order $p^4$ with Some Additional Properties. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 3, pp. 53-69. http://geodesic.mathdoc.fr/item/VNGU_2013_13_3_a4/

[1] Antipkin V. G., Elizarov V. P., “Koltsa poryadka $p^3$”, Sib. mat. zhurn., 23:4 (1982), 9–18 | MR | Zbl

[2] Elizarov V. P., Nenilpotentnye konechnye koltsa, Dep. VINITI, No 1472-85

[3] Corbas B., Williams G. D., “Rings of Order $p^5$. I: Nonlocal Rings”, J. of Algebra, 231 (2000), 677–690 | DOI | MR | Zbl

[4] Corbas B., Williams G. D., “Rings of Order $p^5$. II: Local Rings”, J. of Algebra, 231 (2000), 691–704 | DOI | MR | Zbl

[5] Zhuravlev E. V., “Lokalnye koltsa poryadka $p^6$ c 4-nilpotentnym radikalom Dzhekobsona”, Sibirskie elektronnye matematicheskie izvestiya, 3 (2006), 15–59 http://semr.math.nsc.ru | MR | Zbl

[6] Kruse R. L., Price D. T., Nilpotent Rings, Gordon and Breach, 1969 | MR | Zbl

[7] Nechaev A. A., “Finite Rings with Applications”, Handbook of Algebra, 5, 2008, 1–119 | DOI | MR

[8] Stanley R. P., “Zero-Square Rings”, Pacific J. Math., 30:3 (1969), 811–824 | DOI | MR | Zbl

[9] Elizarov V. P., Konechnye koltsa, Gelios ARV, M., 2006