# On the Structure of the Generalized Group of Units

@inproceedings{Kadri2020OnTS, title={On the Structure of the Generalized Group of Units}, author={Therrar Kadri and Mohammad El-Hindi}, year={2020} }

Let R be a finite commutative ring with identity and U(R) be its group of units. In 2005, El-Kassar and Chehade presented a ring structure for U(R) and as a consequence they generalized this group of units to the generalized group of units U (R) defined iteratively as the group of the units of U(R), with U (R) = U(R). In this paper, we examine the structure of this group, when R = Zn. We find a decomposition of U (Zn) as a direct product of cyclic groups for the general case of any k, and we… Expand

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On The Generalized Multiplicative Euler Phi Function

- Mathematics
- 2021

The generalized group of units of the ring modulo n was first introduced by El-Kassar and Chehade, written as Uk(Zn). This allows us to formulate a new generalization to the Euler phi function φ(n),… Expand

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