We introduce two kinds of new variations of dominant dimensions, which have some advantages in the study of gendo-Gorenstein algebras. One is the $\nu$-stably dominant dimension associated to the Nakayama functor $\nu$. Using it, a criterion for an algebra being gendo-Gorenstein is given, and the gendo-Gorensteiness of algebras are invariant under left-split extensions. Moreover, the difference of the $\nu$-stably dominant dimension is bounded for two derived equivalent gendo-Gorentein algebras. The other is a dominant dimension building from the Gorenstein balance module. An upper bound of this kind of dominant dimension is given for gendo-Gorenstein algebras.
GAO Nan
,
ZHANG Juxia
,
MA Jing
. On dominant dimensions of gendo-Gorenstein algebras[J]. Journal of Shanghai University, 2026
, 32(2)
: 333
-339
.
DOI: 10.12066/j.issn.1007-2861.2394
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