Geodesic
On the classification of finite commutative local rings
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 625-638.

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In this article we classified up to isomorphism all finite commutative local ring with Jacobson radical $ J $ the index of nilpotency four and conditions: $$\mathrm{char}\, R=2,\ \dim_{R/J} J/J^2=2,\ \dim_{R/J} J^2/J^3=2,\ \dim_{R/J} J^3=1.$$
Keywords: finite rings, local rings. 
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E. V. Zhuravlev. On the classification of finite commutative local rings. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 625-638. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a20/

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

[2] V. P. Elizarov, Nenilpotentnye konechnye koltsa, Rukopis dep. v SO AN SSSR, No 1472:85, Redkollegiya Sibirskogo matematicheskogo zhurnala, 1985

[3] V. A. Ratinov, Polusovershennye koltsa so spetsialnymi tipami prisoedinennykh grupp, Dis. ... kand. fiz.-mat. nauk, M., 1980

[4] J. B. Derr, G. F. Orr, P. S. Peck, “Noncommutative rings of order $p^4$”, Journal of Pure and Applied Algebra, 97 (1994), 109–116 | DOI | MR | Zbl

[5] B. Sorbas, G. D. Williams, “Rings of order $p^5$. 1: Nonlocal rings”, J. Algebra, 231 (2000), 677–690 | DOI | MR

[6] B. Sorbas, G. D. Williams, “Rings of order $p^5$. 2: Local rings”, J. Algebra, 231 (2000), 691–704 | DOI | MR

[7] B. Corbas, “Rings with few zero divizors”, Math. Ann., 45 (1969), 1–7 | DOI | MR

[8] B. Corbas, “Finite rings in which the product of any two zero divisors is zero”, Archiv der Math., 21 (1970), 466–469 | DOI | MR | Zbl

[9] C. J. Chikunji, “On a Class of finite rings”, Communication in Algebra, 27:10 (1999), 5049–5081 | DOI | MR | Zbl

[10] E. V. Zhuravlev, “Local rings of order $p^6$ with 4-nilpotent radical of Jacobson”, Siberian Electronic Mathematical Reports, 3 (2006), 15–29 | MR

[11] E. V. Zhuravlev, “About classification finite local rings characteristics $p^2$, Jacobson radical which has an index of nilpotency four”, The news of Altai state university, 1:57 (2008), 18–28

[12] E. V. Zhuravlev, “About izomorphism of finite local rings of characteristics $p^2$, Jacobson radical which has an index of nilpotency four”, The news of Altai state university, 1:61 (2009), 10–16

[13] B. Sorbas, G. D. Williams, “Congruence of two-dimensional subspaces in $M_2(K)$ (characteristic 2)”, Pacific Journal of Mathematics, 188:2 (1999), 237–249 | DOI | MR