Ideals and congruences in $L$-algebras and pre-$L$-algebras

Articles in Press

Document Type : Research Paper

Authors

1 Institut de Recherche en Math\'{e}matique et Physique, Universit\'{e} catholique de Louvain, 1348 Louvain-la-Neuve, Belgique.

2 Dipartimento di Matematica ``Tullio Levi-Civita'', Universit\`a di Padova, 35121 Padova, Italy.

3 Department of Mathematics and Scientific Computing, University of Graz, 8010 Graz, Austria

10.48308/cgasa.2024.232671.1419

Abstract

    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.

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 08 November 2024

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