Minimal representation-infinite artin algebras
1994 ◽
Vol 116
(2)
◽
pp. 229-243
◽
Keyword(s):
Let A be an artin algebra over a commutative artin ring R, mod A be the category of finitely generated right A-modules, and rad∞ (modA) be the infinite power of the Jacobson radical rad(modA) of modA. Recall that A is said to be representation-finite if mod A admits only finitely many non-isomorphic indecomposable modules. It is known that A is representation-finite if and only if rad∞ (mod A) = 0. Moreover, from the validity of the First Brauer–Thrall Conjecture [26, 2] we know that A is representation-finite if and only if there is a common bound on the length of indecomposable modules in mod A.
1980 ◽
Vol 32
(2)
◽
pp. 342-349
◽
1978 ◽
Vol 30
(4)
◽
pp. 817-829
◽
2019 ◽
Vol 18
(10)
◽
pp. 1950193
Keyword(s):
1979 ◽
Vol 31
(5)
◽
pp. 942-960
◽
2011 ◽
Vol 10
(03)
◽
pp. 475-489
◽
Keyword(s):
2003 ◽
Vol 1
(1)
◽
pp. 108-122
◽
1979 ◽
Vol 28
(3)
◽
pp. 335-345
◽
2019 ◽
Vol 62
(3)
◽
pp. 733-738
◽
Keyword(s):
Keyword(s):