A Note on Invariant Basis Number and Types for Strongly Graded Rings - Quang Loc, Nguyen (VNU Journal of Science: Mathematics - Physics; Vol 37 No 1DO - 10.25073/2588-1124/vnumap.4507, 2021)
: Given any pair of positive integers (n, k) and any nontrivial finite group G, we show that there exists a ring R of type (n, k) such that R is strongly graded by G and the identity component R e has Invariant Basis Number. Moreover, for another pair of positive integers (n', k') with n ≤ n' and k | k', it is proved that there exists a ring R of type (n, k) such that R is strongly graded by G and R e has type (n', k'). These results were mentioned in [G. Abrams, Invariant basis number and types for strongly graded rings, J. Algebra 237 (2001) 32-37] without proofs.