# The endomorphisms algebra of translations group and associative unitary ring of trace-preserving endomorphisms in affine plane

## DOI:

https://doi.org/10.22199/issn.0717-6279-2020-04-0051## Keywords:

Affine plane, Endomorphisms, Trace-preserving endomorphisms, Translation group, Aditive group, Associative ring## Abstract

*A description of Endomorphisms of the translation group is introduced in an affine plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and present the Endomorphism algebra thereof will distinguish the Trace-preserving endomorphism algebra in affine plane, and prove that the set of Trace-preserving endomorphism associated with the ’addition’ action forms a commutative group. We also try to prove that the set of trace-preserving endomorphism, together with the two actions, in it, ’addition’ and ’composition’ forms an associative and unitary ring.*

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## Published

## How to Cite

*Proyecciones (Antofagasta, On line)*, vol. 39, no. 4, pp. 821-834, Jul. 2020.

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Copyright (c) 2020 Orgest Zaka, Mohanad. A. Mohammed

This work is licensed under a Creative Commons Attribution 4.0 International License.