A Note on Invariant Basis Number and Types for Strongly Graded Rings
Keyword(s):
: 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 Re 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 Re 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.
2019 ◽
Vol 19
(09)
◽
pp. 2050165
◽
Keyword(s):
1983 ◽
Vol 28
(1)
◽
pp. 101-110
◽
1957 ◽
Vol 8
(2)
◽
pp. 322-322
◽
2002 ◽
Vol 01
(03)
◽
pp. 267-279
◽
2013 ◽
Vol 23
(01)
◽
pp. 81-89
◽
1997 ◽
Vol 55
(2)
◽
pp. 255-259
◽
2001 ◽
Vol 131
(5)
◽
pp. 1163-1166
Keyword(s):
2019 ◽
Vol 18
(05)
◽
pp. 1950086
◽