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Noncommutative rings of order $p\sp 4$. (English) Zbl 0821.16024
From the authors’ abstract: “This paper describes all the isomorphism classes of noncommutative rings with unity and order $p\sp 4$. It is shown that for an odd prime $p$ there are $p + 8$ distinct classes of rings with characteristic $p$ and $p + 4$ classes for characteristic $p\sp 2$. For $p = 2$ there are 9 classes for characteristic 2 and 4 classes for characteristic 4.” The description of commutative finite rings follows from the characterization of completely primary finite rings obtained by {\it R. S. Wilson} [Pac. J. Math. 53, 643-649 (1974; Zbl 0317.16008)].

16P10Finite associative rings and finite-dimensional algebras
Full Text: DOI
[1] Antipkin, V. G.; Elizarov, V. P.: Rings of order p3. Sibirsk, mat. Zh. 23, No. 4, 9-18 (1982) · Zbl 0497.16009
[2] Flor, W.; Wiesenbauer, J.: Zum klassifikationsproblem endlicher ringe, osterreich. Akad. wiss. Math. -natur. Kl. sitzungsber. II 183, 309-320 (1975) · Zbl 0324.16018
[3] Gilmer, R.; Mott, J.: Associative rings of order p3. Proc. Japan acad. 49, 795-799 (1973) · Zbl 0309.16015
[4] Ion, I. D.: Mutually nonisomorphic unitary fp-algebras of order p4. ”Al. I. cuza” iazi sect. I a mat. (N.S) 31, 61-63 (1985)
[5] Kruse, R.; Price, D.: Nilpotent rings. (1969) · Zbl 0198.36102
[6] Mcdonald, B. R.: Finite rings with identity. (1974) · Zbl 0294.16012
[7] Raghavendran, R.: Finite associative rings. Compositio math. 21, 195-229 (1969) · Zbl 0179.33602
[8] Raghavendran, R.: A class of finite rings. Compositio math. 22, 49-57 (1970) · Zbl 0212.37901
[9] Sychowicz, A.: On the embedding of finite rings into matrices. Acta math. Hungar. 46, 269-273 (1985) · Zbl 0591.16010
[10] Szele, T.: Ein satz über die struktur der endliche ringe. Acta sci. Math. Szeged 13, 246-250 (1949) · Zbl 0031.00902
[11] Wilson, R. S.: On the structure of finite rings. Compositio math. 26, 79-93 (1973) · Zbl 0248.16009
[12] Wilson, R. S.: Representations of finite rings. Pacific J. Math. 53, 643-649 (1974) · Zbl 0317.16008