Agradecimentos: The authors thank the anonymous referee for her/his valuable comments that improved the exposition of the paper. C. Fideles was partially supported by CNPq Grant No. 305651/2021-8, by FAPESP Grant Nos. 2019/12498-0 and 2023/04011-9. A. Guimarães was supported by CNPq Grant No. 404851/2021-5 and by FAPESQ-PB Grant No. 2021/3176 Ver menos

Abstract: Let E be the infinite-dimensional Grassmann algebra over an infinite field F of characteristic different from 2. The main purpose of this paper is to describe the [Formula: see text]-ideal of the graded polynomial identities and the [Formula: see text]-space of the central polynomials of E equipped with its [Formula: see text] and 3-induced [Formula: see text]-gradings. Therefore, we generalize the results of [A. Brandão, C. Fidelis and A. Guimarães, [Formula: see text]-gradings of full support on the Grassmann algebra, J. Algebra 601 (2022) 332–353; C. Fidelis, A. Guimarães and P. Koshlukov, A note on [Formula: see text]-gradings on the Grassmann algebra and elementary number theory, Linear Multilinear Algebra 71(7) (2023) 1244–1264] in the PI theory context Ver menos