Geodesic
Endomorphism Semigroups of Sums of Rings
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 247-250

Voir la notice de l'article provenant de la source Cambridge University Press

Let R= 〈R, +, •〉 be the cartesian sum of the rings Ri , i= 1, 2,..., n denoted by , and recall that R is a ring under the componentwise operations. It is well-known (e.g. [1], p. 212) that the endomorphisms of the group 〈R, + 〉 form a ring HomZR (under function addition and composition) and moreover HomZR is isomorphic to the matrix ring under the usual matrix operations of addition and multiplication. 
Maxson, Carlton J. Endomorphism Semigroups of Sums of Rings. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 247-250. doi: 10.4153/CMB-1974-048-7
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[1] 1. Fuchs, L., Abelian Groups, Pergamon Press, New York, 1967. Google Scholar

[2] 2. Goldhaber, J. and Ehrlich, G., Algebra, The Macmillan Company, New York, 1970. Google Scholar

[3] 3. Herstein, I., Noncommutative Rings, Cams Monograph No. 15, MAA, 1968. Google Scholar

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