Centralizer near-rings that are endomorphism rings

Authors:
Carlton J. Maxson and Kirby C. Smith

Journal:
Proc. Amer. Math. Soc. **80** (1980), 189-195

MSC:
Primary 16A76; Secondary 16A44

MathSciNet review:
577742

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Abstract: For a finite ring *R* with identity and a finite unital *R*-module *V* the set for all is the centralizer near-ring determined by *R* and *V*. Those rings *R* such that is a ring for every *R*-module *V* are characterized. Conditions are given under which is a semisimple ring. It is shown that if is a semisimple ring then .

**[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]**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**[3]**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**[4]**Carlton J. Maxson and Kirby C. Smith,*The centralizer of a set of group automorphisms*, Comm. Algebra**8**(1980), no. 3, 211–230. MR**558111**, 10.1080/00927878008822455**[5]**Carlton J. Maxson and Kirby C. Smith,*Simple near-ring centralizers of finite rings*, Proc. Amer. Math. Soc.**75**(1979), no. 1, 8–12. MR**529202**, 10.1090/S0002-9939-1979-0529202-X**[6]**-,*Near-ring centralizers*, Proc. Ninth Annual USL Math. Conf. Research Series 48, Univ. Southwestern Louisiana, April, 1979, pp. 49-58.**[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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DOI:
https://doi.org/10.1090/S0002-9939-1980-0577742-8

Keywords:
Centralizers,
near-rings,
semisimple rings

Article copyright:
© Copyright 1980
American Mathematical Society