Argerami, Martin; Szechtman, Fernando; Tifenbach, Ryan On Tate’s trace. (English) Zbl 1130.15001 Linear Multilinear Algebra 55, No. 6, 515-520 (2007). Let \(V\) be a vector space over a given field. An endomorphism \(\varphi\) of \(V\) is finite potent if \(\varphi^m(V)\) is finite dimensional, for some positive integer \(m\). J. Tate [Ann. Sci. Éc. Norm. Supér. (4) 1, No. 1, 149–159 (1968; Zbl 0159.22702)] extended the traditional definition of trace, including any underlined vector space, provided the given endomorphism is finite potent. The problem of whether the Tate’s trace is linear remains open. In this paper, a new approach to this problem is provided and it is shown that if a counterexample to linearity exists at all, it must be of a special type. Reviewer: C. M. da Fonseca (Coimbra) Cited in 25 Documents MSC: 15A04 Linear transformations, semilinear transformations 15A03 Vector spaces, linear dependence, rank, lineability Keywords:finite potent endomorphism Citations:Zbl 0159.22702 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Pablos Romo F, Linear Multilinear Algebra [2] Tate J., Annales Scientifiques de l’Ecole Normale Superieure Series 4 1 pp 149– (1968) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.