Geodesic
A Note on Endomorphism Semigroups
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 47-48

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If is a universal algebra, the set of endomorphisms of forms a monoid (i.e., semigroup with identity) under composition. We denote it by End (). For definitions and notations, see [1]. It is well known (e.g., [1], Theorem 12.3) that for any monoid M there is a unary algebra with M ≅ End (). E. Mendelsohn and Z. Hedrlin [3] have proved that the monoid of a subalgebra of an algebra is independent of the monoid of . In [2], Hedrlin proves the same for the monoid of a homomorphic image of . The proofs of these depend heavily on graph-theoretical and category-theoretical considerations. In this note considerably shorter direct algebraic proofs are given of these results. 
Platt, Craig. A Note on Endomorphism Semigroups. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 47-48. doi: 10.4153/CMB-1970-008-2
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     title = {A {Note} on {Endomorphism} {Semigroups}},
     journal = {Canadian mathematical bulletin},
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     year = {1970},
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     number = {1},
     doi = {10.4153/CMB-1970-008-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-008-2/}
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