Simple near-ring centralizers of finite rings
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- by Carlton J. Maxson and Kirby C. Smith PDF
- Proc. Amer. Math. Soc. 75 (1979), 8-12 Request permission
Abstract:
For a finite ring R with identity and a finite unital R-module V we call $C(R) = \{ f:V \to V|f(\alpha v) = \alpha f(v)$ for all $\alpha \in R,v \in V\}$ the near-ring centralizer of R. We investigate the structure of $C(R)$ and obtain a characterization of those rings R for which $C(R)$ is a simple nonring.References
- G. Betsch, Some structure theorems on $2$-primitive near-rings, Rings, modules and radicals (Proc. Colloq., Keszthely, 1971) Colloq. Math. Soc. János Bolyai, Vol. 6, North-Holland, Amsterdam, 1973, pp. 73–102. MR 0360722
- I. N. Herstein, Noncommutative rings, The Carus Mathematical Monographs, No. 15, Mathematical Association of America; distributed by John Wiley & Sons, Inc., New York, 1968. MR 0227205
- Nathan Jacobson, Structure of rings, Revised edition, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, Providence, R.I., 1964. MR 0222106
- Carlton J. Maxson and Kirby C. Smith, The centralizer of a group automorphism, J. Algebra 54 (1978), no. 1, 27–41. MR 511455, DOI 10.1016/0021-8693(78)90019-4
- Carlton J. Maxson and Kirby C. Smith, The centralizer of a group endomorphism, J. Algebra 57 (1979), no. 2, 441–448. MR 533806, DOI 10.1016/0021-8693(79)90231-X —, The centralizer of a set of group automorphisms (preprint).
- Bernard R. McDonald, Finite rings with identity, Pure and Applied Mathematics, Vol. 28, Marcel Dekker, Inc., New York, 1974. MR 0354768
- Günter Pilz, Near-rings, North-Holland Mathematics Studies, No. 23, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. The theory and its applications. MR 0469981
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 8-12
- MSC: Primary 16A76
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529202-X
- MathSciNet review: 529202