… Another motivation for Theorem 3.3 is to obtain a characterization of Gorenstein local rings
via … several criteria for Gorenstein local rings via syzygy modules of the residue field over CM …

… theorem, we can find a complete regular local ring (A, mA,k) and a … Moreover, for Gorenstein
rings, the syzygy functor Ω … We denote by vK the value group and by Kv the residue field of (K…

… the residue field of each commutative Noetherian local ring has … similar important
characterizations of local rings via other … To establish the sequence in (2.10.1), we consider a …

… homomorphic images of syzygy modules of the residue field. … If the residue field k is finite,
then we use the standard trick to … obtain a characterization of Gorenstein local rings provided …

… We prove that Ulrich modules over CM local rings have … We may assume that the residue
field k is infinite. In the base case, … , Characterizations of regular local rings via syzygy modules …

… the residue field of each commutative Noetherian local ring … similar important characterizations
of local rings via other … it is a syzygy of a maximal Cohen–Macaulay module. Consequently…

… give several characterizations of almost Gorenstein rings in … two with algebraically closed
residue field. Then A has a … of M and by M the (first) syzygy of M in the minimal free resolution. …

… -th syzygy module in … characterizing Gorenstein local rings via reducing G-dimension. In
the following, for given subcategories X ,Y of modR, denote by X ∗Y the collection of all modules …

… a noetherlan local ring with maximal Ideal m and residue field £ … R + 1)'st syzygy of a module
with bounded Betti numbers is … , and admit a variety of possible characterizations, cf. [43, 19]…

… residue field k and Cohen-Macaulay associated graded ring grm(R… an MCM module over a
Gorenstein complete local ring R is … R-module satisfies the SCr-condition when its first syzygy …