Preserving of covers by hopf invariants

Gorenstein injective and projective modules and actions of finite-dimensional Hopf algebras

“…[9, Section 9.1]). In this way, the last result extends [7, Theorem 1.2] and [12,Theorem 4.3]. Examples of non-noetherian Gorenstein rings can be found in [6].…”

“…These include categories of modules over IwanagaGorenstein rings, i.e., left and right noetherian rings such that both left and right injective dimensions of the ring are finite, [13]. In [7,Theorem 1.2] it is shown that when R is Iwanaga-Gorenstein then the fixed ring R G by the action of a finite group G is also Iwanaga-Gorenstein or more generally, in [12,Theorem 4.3], if A is an H-module algebra which is Iwanaga-Gorenstein, then A H is IwanagaGorenstein.…”

“…Lately this problem was treated (among others) for the case of relative injective covers over Hopf extensions ( [12]) and for Gorenstein modules over graded rings ([1]). In the aforementioned works, separability conditions of the involved functors (cf.…”

On Covers and Envelopes under Hom and Tensor Functors

“…In [11][12][13], García Rozas and Torrecillas investigated when a covariant functor F preserves (resp. reflects) (pre)covers, i.e., if…”

Invariants of FP-Projective Dimensions Under Cleft Extensions

“…A left A-module M is said to be a Hopf module if it has a right H * -comodule structure satisfying the compatibility condition ρ M (am) = a (0) m (0) ⊗ a (1) Recall the induction and coinduction functors defined as follows (see [7]):…”