Simple near-ring centralizers of finite rings

Authors:
Carlton J. Maxson and Kirby C. Smith

Journal:
Proc. Amer. Math. Soc. **75** (1979), 8-12

MSC:
Primary 16A76

MathSciNet review:
529202

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Abstract: For a finite ring *R* with identity and a finite unital *R*-module *V* we call for all the near-ring centralizer of *R*. We investigate the structure of and obtain a characterization of those rings *R* for which is a simple nonring.

**[1]**G. Betsch,*Some structure theorems on 2-primitive near-rings*, Rings, modules and radicals (Proc. Colloq., Keszthely, 1971) North-Holland, Amsterdam, 1973, pp. 73–102. Colloq., Math. Soc. János Bolyai, Vol. 6. MR**0360722****[2]**I. N. Herstein,*Noncommutative rings*, The Carus Mathematical Monographs, No. 15, Published by The Mathematical Association of America; distributed by John Wiley & Sons, Inc., New York, 1968. MR**0227205****[3]**Nathan Jacobson,*Structure of rings*, American Mathematical Society Colloquium Publications, Vol. 37. Revised edition, American Mathematical Society, Providence, R.I., 1964. MR**0222106****[4]**Carlton J. Maxson and Kirby C. Smith,*The centralizer of a group automorphism*, J. Algebra**54**(1978), no. 1, 27–41. MR**511455**, 10.1016/0021-8693(78)90019-4**[5]**Carlton J. Maxson and Kirby C. Smith,*The centralizer of a group endomorphism*, J. Algebra**57**(1979), no. 2, 441–448. MR**533806**, 10.1016/0021-8693(79)90231-X**[6]**-,*The centralizer of a set of group automorphisms*(preprint).**[7]**Bernard R. McDonald,*Finite rings with identity*, Marcel Dekker, Inc., New York, 1974. Pure and Applied Mathematics, Vol. 28. MR**0354768****[8]**Günter Pilz,*Near-rings*, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. The theory and its applications; North-Holland Mathematics Studies, No. 23. MR**0469981**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0529202-X

Keywords:
Centralizers,
simple rings,
near-rings

Article copyright:
© Copyright 1979
American Mathematical Society