A Note on Endomorphism Semigroups
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 47-48
Voir la notice de l'article provenant de la source Cambridge University Press
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
@article{10_4153_CMB_1970_008_2,
author = {Platt, Craig},
title = {A {Note} on {Endomorphism} {Semigroups}},
journal = {Canadian mathematical bulletin},
pages = {47--48},
year = {1970},
volume = {13},
number = {1},
doi = {10.4153/CMB-1970-008-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-008-2/}
}
[1] 1. Grätzer, G., Universal Algebra, Van Nostrand, 1968. Google Scholar
[2] 2. Hedrlín, Z., On endomorphisms of graphs and their homomorphic images, to appear in Proof Techniques in Graph Theory, forthcoming, Academic Press. Google Scholar
[3] 3. Hedrlín, Z., and Mendelsohn, E., On the category of graphs with a given subgraph, to appear in the Canadian Journal of Mathematics. Google Scholar
[4] 4. Hedrlín, Z., and Pultr, A., On full embeddings of categories of algebras, Illinois Journal of Mathematics 10 (1966), 392-406. Google Scholar
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