… (injective) modules and Gorenstein homological dimensions along Frobenius extension of
rings. The theory of Frobenius extensions was developed by Kasch [18] as a generalization of …

… (or injective) dimension is n for … -Frobenius extension of R and show it also is a Gorenstein
ring. Further we generalize [3, Corollary 8 and 8'] to the case of a quasi-Frobenius extension. …

… to our present generalized case; we shall also exceed [4], [6] somewhat in considering
injective and weak dimensions. On the other hand, we restrict ourselves, in the present work, to …

… primarily with Noetherian rings whose self injective dimension is finite. Thus, … injective
dimension one, can be regarded as a one dimensional analogue of the theory of quasi-Frobenius …

… the left minimum conditions does not always possess an injective left module Q of the above
… ], while every finite-dimensional algebra A as well as every quasi-Frobenius ring A certainly …

… We show that the Frobenius parts of Frobenius extensions are again Frobenius extensions.
Furthermore, let A and B … By a flat-injective module we mean a module which is both flat and …

… Frobenius extensions in such generalized sense. Thus we first study relative homological
dimensions … of relatively projective and relatively injective modules as well as Hirata's [6] results…

… Gorenstein injective (projective) if and only if A⊗R M and HomR(A, M) are Gorenstein injective
(… to study some properties of Ding injective modules along Frobenius extensions of rings. …

… dimensional modules, we seek to associate to a possibly infinite dimensional module M of a
Frobenius … 0 is an injective resolution of M of smaller length than the original one. Thus, M is …

… objects and enough injective objects, the supremum of the Gorenstein projective dimension
of all objects coincides with the supremum of the Gorenstein injective dimension of all …