Abstract
Let E be the infinite dimensional Grassmann algebra over an infinite field of characteristic different from 2. Let be a n-induced -grading on E and let be its support. In this paper, we study the properties of the set as a subset of Assuming that this set is bounded, we describe the graded identities of the respective graded algebra. We also show that is a subgroup of if and only if it is cyclic, and we describe the graded identities in this case.
Acknowledgments
We thank Claudemir Fidelis for the useful discussions and for his valuable comments. Additionally, we are grateful to the anonymous referee for his/her useful comments and suggestions which helped us to substantially clarify and improve the manuscript.