#### Glasnik Matematicki, Vol. 43, No.1 (2008), 25-40.

### AUTOMORPHISM GROUPS OF FINITE RINGS OF CHARACTERISTIC
*p*^{2} AND *p*^{3}

### Chiteng'a John Chikunji

Department of Basic Sciences, Botswana College of Agriculture, Gaborone, Botswana

*e-mail:* `jchikunj@bca.bw`

**Abstract.** In this paper we describe the group of automorphisms of
a completely primary finite ring *R* of characteristic *p*^{2} or
*p*^{3}
with Jacobson radical J
such that J^{3}=(0),
J^{2} ≠ (0);
the annihilator of
J coincides with
J^{2};
and the maximal Galois (coefficient) subring
*R*_{0} of *R* lies in the center of *R*.

**2000 Mathematics Subject Classification.**
16N10, 20B25, 16N40, 15A03.

**Key words and phrases.** Completely primary
finite ring, automorphism group, Galois ring.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.43.1.04

**References:**

- C. J. Chikunji,
*Automorphisms of completely primary
finite rings of characteristic **p*, Colloq. Math. **111** (2008), 91-113.

MathSciNet

- C. J. Chikunji,
*On a Class of Finite Rings*,
Comm. Algebra **27** (1999), 5049-5081.

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CrossRef

- C. J. Chikunji,
*A classification of cube zero radical
completely primary finite rings*,
Demonstratio Math. **38** (2005), 7-20.

MathSciNet

- W. E. Clark,
*A coefficient ring for finite
non-commutative rings*,
Proc. Amer. Math. Soc. **33** (1972), 25-28.

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CrossRef

- R. Raghavendran,
*Finite associative rings*,
Compositio Math. **21** (1969), 195-229.

MathSciNet

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