Geodesic
Integral classification of endomorphisms of an arbitrary algebra with finitary operations
Algebra i logika, Tome 63 (2024) no. 1, pp. 58-76

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@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/}
}
TY  - JOUR
AU  - A. V. Litavrin
TI  - Integral classification of endomorphisms of an arbitrary algebra with finitary operations
JO  - Algebra i logika
PY  - 2024
SP  - 58
EP  - 76
VL  - 63
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2024_63_1_a4/
LA  - ru
ID  - AL_2024_63_1_a4
ER  - 
%0 Journal Article
%A A. V. Litavrin
%T Integral classification of endomorphisms of an arbitrary algebra with finitary operations
%J Algebra i logika
%D 2024
%P 58-76
%V 63
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2024_63_1_a4/
%G ru
%F 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/