On the Unit Groups of a Class of Total Quotient Rings of Characteristic p k with k ≥ 3

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International Journal of Algebra

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Let R be a commutative completely primary finite ring. The struc tures of the groups of units for certain classes of R have been determined. It is well known that completely primary finite rings play a crucial role in the endeavors towards the classification of finite rings. Let G be an arbitrary finite group. The classification of all finite rings Ri so that U(Ri) ∼= G is still an open problem. In this paper, we consider S ⊂ R to be a saturated multiplicative subset of R and construct a total quotient ring RS whose group of units is characterized, when char RS = p k , k ≥ 3. It is observed that U(R) ∼= U(RS), since R ∼= RS. The cases when char RS = p k , k = 1, 2 have been studied in a related work.

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On the Unit Groups of a Class of Total Quotient Rings of Characteristic p k with k ≥ 3

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Wekesa, W. A., Oduor, O. M., Aywa, S., & Onyango, O. M. (2017). On the Unit Groups of a Class of Total Quotient Rings of Characteristic pk with k≥ 3. International Journal of Algebra, 11(3), 127-135.

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