Pith. sign in

REVIEW 1 cited by

A Frattini theory for evolution algebras

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2507.01935 v1 pith:2MKZTT5R submitted 2025-07-02 math.RA

Manuel Ladra , Andrés Pérez-Rodríguez This is my paper
classification math.RA
keywords frattiniidealalgebrasevolutionnilradicalsubalgebratheoryalternative
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

This paper develops a Frattini theory for evolution algebras defining the Frattini subalgebra as the intersection of all maximal subalgebras, and the Frattini ideal as the largest ideal contained in it. To this end, we revisit the notion of nilradical, whose classical definition is not directly applicable in this setting, and propose the supersolvable nilradical as a suitable alternative. This leads to necessary and sufficient conditions for the triviality of the Frattini subalgebra and ideal. Finally, we also briefly examine the relevance of the Frattini ideal in the study of dually atomistic evolution algebras.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Nilpotency and Frattini theory for transposed Poisson algebras

    math.RA 2026-04 unverdicted novelty 6.0 of 10

    Finite-dimensional transposed Poisson algebras are nilpotent exactly when left multiplications are nilpotent in both associative and Lie operations, with the nilpotent radical equaling the associative radical and Frat...

Pith tools