Integral classification of endomorphisms of an arbitrary algebra with finitary operations
Algebra i logika, Tome 63 (2024) no. 1, pp. 58-76
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We introduce a bipolar classification with index $j$ for endomorphisms of an arbitrary $n$-groupoid with $n>1$, where $j=1,2,\ldots,n$. The classifications of endomorphisms constructed generalize the bipolar classification of endomorphisms of an arbitrary groupoid (i.e., a $2$-groupoid) introduced previously. Using a left bipolar classification of endomorphisms of an $n$-groupoid (a particular case of the obtained classifications), we succeed in constructing an integral classification of endomorphisms of an arbitrary algebra (i.e., a structure without relations) with finitary operations.
Keywords:
integral classification, bipolar classification, algebra.
Mots-clés : endomorphism, groupoid
Mots-clés : endomorphism, groupoid
@article{AL_2024_63_1_a4,
author = {A. V. Litavrin},
title = {Integral classification of endomorphisms of an arbitrary algebra with finitary operations},
journal = {Algebra i logika},
pages = {58--76},
publisher = {mathdoc},
volume = {63},
number = {1},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AL_2024_63_1_a4/}
}
A. V. Litavrin. Integral classification of endomorphisms of an arbitrary algebra with finitary operations. Algebra i logika, Tome 63 (2024) no. 1, pp. 58-76. http://geodesic.mathdoc.fr/item/AL_2024_63_1_a4/