Let $(A,\mathfrak {m}) $ be a short Artin local ring (ie, $\mathfrak {m}^ 3= 0$ and $\mathfrak
{m}^ 2\neq 0$). Assume $ A $ is not a hypersurface ring. We show there exists $ c_A\geq 2 …

It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric
Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten …

On Special Fiber Rings of Modules Page 1 http://dx.doi.org/. /CJM-- ©Canadian Mathematical
Society On Special Fiber Rings of Modules Cleto B. Miranda-Neto Abstract. We prove results …

In this paper we mainly study the properties of dual modules over k-Gorenstein rings. For a k-
Gorenstein ring Λ we show that the right self-injective dimension is less than or equal to k if …

We prove that for a left and right Noetherian ring $ R $, $ _RR $ satisfies the Auslander
condition if and only if so does every flat left $ R $-module, if and only if the injective …

In this paper, we investigate the maximal Cohen–Macaulay property of tensor products of
modules, and then give criteria for projectivity of modules in terms of vanishing of Ext …

We obtain some methods to construct a (strongly) proper resolution (resp. coproper
coresolution) of one end term in a short exact sequence from that of the other two terms. By …

In this paper we extend two results of Happel to commutative rings. Let $(A,\mathfrak {m}) $
be a commutative Noetherian local ring. Let $ D^ b_f (mod\A) $ be the bounded derived …

In case A has finite Krull-dimension, say d, it is well-known by Bass [2] that A is a Gorenstein
ring if and only if ExtiA (M, A)=(0) for every finitely generated A-module M and for every …

We address the problem of when the tensor product of two finitely generated modules over a
Cohen-Macaulay local ring is Ulrich in the generalized sense of Goto et al., and in particular …