Corbas, B.; Williams, G. D. Rings of order \(p^5\). I: Nonlocal rings. (English) Zbl 1017.16014 J. Algebra 231, No. 2, 677-690 (2000). Summary: In this paper and its sequel, the structure and classification up to isomorphism of all finite rings of order \(p^5\) are determined. The theory of semiperfect rings is here applied to deal with the nonlocal rings of this order. In part II [ibid. 691-704 (2000; see the following review Zbl 1017.16015)] we shall treat the local rings. Cited in 3 ReviewsCited in 40 Documents MSC: 16P10 Finite rings and finite-dimensional associative algebras Keywords:finite rings; semiperfect rings; local rings Citations:Zbl 1017.16015 PDFBibTeX XMLCite \textit{B. Corbas} and \textit{G. D. Williams}, J. Algebra 231, No. 2, 677--690 (2000; Zbl 1017.16014) Full Text: DOI References: [1] Behrens, E. A., Ring Theory (1972), Academic Press: Academic Press New York/London [2] Cohn, P. M., Algebra (1991), Wiley: Wiley Chichester [3] Corbas, B., Rings with few zero divisors, Math. Ann., 181, 1-7 (1969) · Zbl 0175.31502 [4] Derr, J. B.; Orr, G. F.; Peck, P. S., Noncommutative rings of order \(p^4\), J. Pure Appl. Algebra, 97, 109-116 (1994) · Zbl 0821.16024 [5] Jacobson, N., Structure of rings. Structure of rings, Amer. Math. Soc. Colloq. Publ., 37 (1956), Amer. Math. Soc: Amer. Math. Soc Providence [6] Jacobson, N., Basic Algebra II (1980), Freeman: Freeman San Francisco · Zbl 0441.16001 [7] Janusz, G. J., Separable algebras over commutative rings, Trans. Amer. Math. Soc., 122, 461-479 (1966) · Zbl 0141.03402 [8] Krull, W., Algebraische theorie der ringe, II, Math. Ann., 91, 1-46 (1924) · JFM 50.0072.01 [9] Lam, T. Y., A first course in noncommutative rings, Grad. Texts in Math. (1991), Springer-Verlag: Springer-Verlag New York · Zbl 0728.16001 [10] Passman, D. S., A Course in Ring Theory (1991), Wadsworth: Wadsworth Belmont · Zbl 0783.16001 [11] Pierce, R. S., Associative algebras, Grad. Texts in Math. (1982), Springer-Verlag: Springer-Verlag New York · Zbl 0497.16001 [12] Raghavendran, R., Finite associative rings, Compositio Math., 21, 195-229 (1969) · Zbl 0179.33602 [13] Williams, G. D., Congruence of (2×2) matrices, Discrete Math. (2000) · Zbl 0999.15022 [14] Wilson, R. S., Representations of finite rings, Pacific J. Math., 53, 643-649 (1974) · Zbl 0317.16008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.