Ideals and congruences in $L$-algebras and pre-$L$-algebras
نویسندگان
1 Department of Mathematics and Scientific Computing, University of Graz, 8010 Graz, Austria
2 Institut de Recherche en Math\'{e}matique et Physique, Universit\'{e} catholique de Louvain, 1348 Louvain-la-Neuve, Belgique.
3 Dipartimento di Matematica ``Tullio Levi-Civita'', Universit\`a di Padova, 35121 Padova, Italy.
doi
10.48308/cgasa.2024.232671.1419چکیده
We link the recent theory of $L$-algebras to previous notions of Universal Algebra and Categorical Algebra concerning subtractive varieties, commutators, multiplicative lattices, and their spectra. We show that the category of $L$-algebras is subtractive and normal in the sense of Zurab Janelidze, but neither the category of $L$-algebras nor that of pre-$L$-algebras are Mal'tsev categories, hence in particular they are not semi-abelian. Therefore $L$-algebras are a rather peculiar example of an algebraic structure.
