… Let ϕ : R −→ R be a local homomorphism of Gorenstein complete local rings … dimensional
cases In this section we assume that the Gorenstein complete local ring (R,m,k) has dimension …

… In particular, for a finitely generated right Λ-module M having Gorenstein dimension zero as
… Since End Λ (M) is a division ring, and since we have an injective ring homomorphism σ: R/…

… We will study homological properties of noetherian rings. As a bridge between the n-Gorenstein
property and the dominant dimension, we will introduce the dominant numbers of rings …

… is a left noetherian ring with id R R<∞ and M is a Gorenstein … with finite flat dimension; if R
is a right noetherian ring with i d … Let ψ:M→L be an R-homomorphism such that fd R L is finite. …

… We may assume that the homomorphism Fi -* Fo is defined by the column vector φ such
that … dimension such that R/a is a Gorenstein ring implies that R itself is a Gorenstein ring. …

… S is a Gorenstein ring of injective dimension one if and only if the total ring of quotients Q of S
is Gorenstein … Drozd-Kirichenko-Roiter 1967 [5] have shown that Gorenstein orders behave …

… In the previous parer [8], we defined a one-dimensional Gorenstein ring R as a … -Gorenstein
and a ring homomorphism is a two-sided flat epimorphism, then S is also a 1-Gorenstein ring…

… Gorenstein injective dimension of R/I as a left R-module are identical. In addition, we prove
that if R → S is a homomorphism of rings … modules, then the Gorenstein flat dimension of S as …

… Then the canonical ring homomorphism R [ t ] ↠ R gives M the structure of an R[t]-module
in the … acquires an R-module structure via the natural monic ring homomorphism R ↣ R [ t ] . …

… A homomorphism ϕ: X → Y of degree i is a sequence of R-linear maps ϕ n :X n … All
homomorphisms of degree i form an Abelian group, denoted Hom R (X,Y) i , that we identify with ∏ …