Tuesday, February 9, 14:00
Carlo Klapproth, Homological dimensions of idempotent subrings
We investigate homological dimensions of idempotent subrings
R in a class of rings including artinian rings.
We continue works by Ingalls and Paquette (see [IP15] and [IP17]) and Bravo and Paquette (see [BP20]).
We establish a homological relationship of the rings
(1-e)R(1-e), the semisimple
M:=eR(1-e) and the graded Yoneda ring
In particular we show for
- how to construct minimal projective resolutions of
(1-e)R(1-e)-modules only using homological properties of
i>0 if the global dimension of
R and the projective dimension of
M are finite and
Y has uniform graded right Loewy length and
- that all sandwiched idempotent subrings
(1-e)R(1-e) ⊂ (1-f)R(1-f) ⊂ R have finite global dimension iff
gldim R < ∞ and all idempotent subrings of
Y have finite global dimension.