zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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)].

MSC:
 16P10 Finite associative rings and finite-dimensional algebras
Full Text:
References:
 [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