Geodesic
Unreduced generalized endoprimal abelian groups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2019), pp. 32-38

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The endofunction on abelian group $A$ is the function $f: A^n\to A$, such that $\varphi f(x_1,\ldots, $ $ x_n) = f(\varphi(x_1),\ldots, \varphi(x_n))$ for all endomorphisms $\varphi$ of group $A$ and all $n $ from $ \mathbb{N}$. If each endofunction has the form $f(x_1,\ldots, x_n) = \sum_{i = 1}^n \lambda_ix_i$ for some central endomorphisms $\lambda_1,\ldots, \lambda_n$ of a group $A$, then such a group is called generalized endoprimal ($GE$-group). In the paper, we find $GE$-groups in the class of nonreduced abelian groups. In addition, results concerning connections of $GE$-groups with abelian groups whose endomorphism rings are unique addition rings have been obtained.
Keywords: abelian group, endofunction, endoprimality, endomorphism ring. 
@article{IVM_2019_11_a3,
     author = {O. V. Lyubimtsev},
     title = {Unreduced generalized endoprimal abelian groups},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {32--38},
     publisher = {mathdoc},
     number = {11},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_11_a3/}
}
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O. V. Lyubimtsev. Unreduced generalized endoprimal abelian groups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2019), pp. 32-38. http://geodesic.mathdoc.fr/item/IVM_2019_11_a3/